HP 6S Owner's Manual
1 HP 6S Scientific Calculator H English.PM6 3/3/99, 3:45 PM 1
2 NOTICE This manual and any examples contained herein are provided as is and are subject to change without notice. Except to the extent prohibited by law , Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manual and specifically disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein. © Hewlett-Packard Company 1999. All rights reserved. REGULA T ORY INFORMA TION USA This calculator has been tested and found to comply with the limits for a Class B digital device, pursuant to part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This calculator generates, uses and can radiate radio frequency energy and may interfere with radio and television reception. In the unlikely event that this equipment does cause interference to radio or television reception, try the following: ⢠reorient or relocate the receiving antenna ⢠increase separation between the calculator and the receiver ⢠consult your dealer or an experienced radio/TV technician for help. CANADA This Class B digital apparatus complies with Canadian ICES-003. Cet appareil numérique de la classe B est conforme à la norme NMB-003. English.PM6 3/3/99, 3:45 PM 2
3 Contents 1. Keyboard 5 General keys 5 Memory keys 5 Special keys 5 Base-n keys 5 Function keys 6 Statistical keys 6 2. The display 7 Exponent displays 7 3. Basic functions 8 Entering numbers 8 Entering negative numbers 8 Entering exponential numbers 8 Arithmetic operator 8 Equals 8 Making corrections 9 Clearing errors 9 Fixing the number of decimal places displayed 9 Setting the display to scientific notation 9 4. Calculations 10 Precision 10 Order of operations 10 Simple calculations 10 Specifying the order of calculations 10 Re-using arithmetic operations 1 1 Using memory 1 1 Fraction arithmetic 1 1 Percentage calculations 12 5. Other functions 13 Converting minutes and seconds to decimal format 13 Conversion between angles, radians and grads 13 T rigonometric functions 13 Hyperbolic functions 14 Logarithmic functions 14 Powers and roots 14 Miscellaneous functions 15 Polar to rectangular coordinates conversions 15 Rectangular to polar coordinates conversions 15 English.PM6 3/3/99, 3:45 PM 3
4 6. Binary , octal and hexadecimal values 16 Binary/octal/decimal/hexadecimal conversions 16 Binary/octal/decimal/hexadecimal calculations 16 Logical operations 17 Radix complement 18 7 . Using statistics 1 9 Entering a list of data items to analyse 1 9 Using statistical functions on your data 19 8 . Specifications 2 0 9 . Changing the battery 2 1 English.PM6 3/3/99, 3:45 PM 4
5 1. Keyboard General keys Key Functions Page 0 to9 : . Data entry 8 -* Basic calculation 8 d= ¡ Reset the calculator 9 and clear the memory à Clear/clear error 9 à Change sign 8 Memory keys Key Functions Page r Retrieve data from the 11 independent memory ´ Store display data in 11 memory ³ Exchange of display data 11 and contents of memory m Add displayed data to 11 memory Special keys Key Functions Page I Inverse 7 M Mode 7 () Brackets (parentheses) 10 ¹ Exponent 8 P Pi 13 Key Functions Page Ãà Sexagesimal/decimal 13 notation conversion ¯ Mode of angle 13 DEG â RADâ GRADâ DEG à Angular conversion of data 13 DEG â RAD â GRAD â DEG ² Register exchange 11 à Clearing the last 9 entered digit ¼ Fix the number of digits 9 after the decimal point » Floating notation 9 ½ Scientific notation 9 ¾ Engineering notation 15 Base-n keys Key Functions Page ¤ Decimal 16 Â¥ Binary 16 ¦ Hexadecimal 16 § Octal 16 A to F Hexadecimal numbers only 16î18 & And 17 o Or 17 x Exclusive Or 17 X Exclusive Nor 17 à Not 17 N Negative 18 Keyboard English.PM6 3/3/99, 3:45 PM 5
6 Function keys K e y Functions Page s Sine 13 c Cosine 13 t T angent 13 S Arc sine 13 ¨ Arc cosine 13 T Arc tangent 13 ª Hyperbolic 14 L Common logarithm 14 à Common antilogarithm 14 à Natural logarithm 14 à Natural antilogarithm 14 à Square root 14 º Square 14 ì Fraction 12 à Cube root 14 à Reciprocal 12 à Factorial 14 K e y Functions Page à Power 8 à Root 14 à Rectangle to polar 15 à Polar to rectangular 15 % Percent 12 Statistical keys Key Functions Page ¿ Statistical data mode 19 à Data entry 19 à Data delete 19 à Sample standard deviation 19 à Population standard deviation 19 à Arithmetic mean 19 n Number of data 19 à Sum of value 19 à Sum of square value 19 Keyboard English.PM6 3/3/99, 3:45 PM 6
7 2. The display INV HYP BIN OCT HE X M E 1 2 . 5 4 3 Mantissa LCD Diagram The display shows input data, interim results and answers to calculations. The mantissa section displays up to 10 digits. The exponent section displays up to ± 99. Display Meaning Page -E- Indicates an error 9 INV I has been pressed to enable inverse key functions 9 M Indicates that data is stored in the memory 1 1 HYP ª has been pressed for hyperbolic functions 14 BIN, OCT , HEX BASE-N mode has been selected 1 6 SD Statistical mode has been selected 19 DEG, RAD, GRAD ¯ has been pressed to switch between the DEG, RAD and GRAD 13 angle types FIX (this does not display) The number of decimal places of a displayed value has been set 9,15 SCI (this does not display) Converts a displayed value to exponent display 9 ENG (this does not display) Converts a displayed value to exponent display of which the exponent 15 is a multiple of 3 and mantissa is between 0 to 999 FLO (this does not display) Convert a SCI or ENG form display to a normal display value 15 45 à 12 à 123 45 12 / 123 11 12. ° 3'45.6" Sexagesimal figure 12 ° 3'45.6" 13 Exponent displays The display can show calculation results only up to 10 digits long. When an intermediate value or a final result is longer than 10 digits, the calculator automatically switches over to exponential notation. V alues greater than 9,999,999,999 are always displayed exponentially . The Display English.PM6 3/3/99, 3:45 PM 7
8 3. Basic functions Entering numbers 123 etc . Entering negative numbers à Press after a number to make it negative. 5.08à -5.08 Entering exponential numbers ¹ Press to enter an exponential number . 3.08Ã10 9 3.08¹9 3.08 09 Arithmetic operator -* dà 4*d - 5 9. Equals = Press to complete your calculation and display a result. If you press = more than once without entering a number , the calculator performs the last arithmetic operation on the value displayed. 4Ã8 4*8= 32. 4*8== 256. Press the number keys to enter numbers. Press . for a decimal point. Press to perform an arithmetic operation on the value displayed. Y ou must enter a number after the arithmetic operator . If you press more than one arithmetic operator in sequence, the calculator only performs the last operation (the last key pressed). Basic functions English.PM6 3/3/99, 3:45 PM 8
9 Making corrections à Press to delete the last number entered. à Press to remove the displayed value, but retain the calculation being performed. Press after the arithmetic operator to cancel the entire calculation. 5 5 5 6Ã5= 20. 5 5 5 Ã= 0. Clearing errors à Press to clear an error (indicated by î-E-î in the display)îeg, an overflow errorîand retain data in the memory . ¡ Press to reset the calculator and clear the memory (solar model only). Fixing the number of decimal places displayed I¼ Press after your arithmetic operation, or after you press ¡ , to set the number of decimal 2 places displayed (the number you press is the number of decimal places you want to display). The calculator rounds the number in the display but maintains full precision internally . I Press to reset the floating decimal point. ¼. Setting the display to scientific not ation I Press to set the display to scientific notation and express the number as a power ofî 10îeg, ½ .0043 is displayed as 4.3. -03 to represent 4.3Ã10 -3 . I Press to reset the display to the floating format. » Basic functions English.PM6 3/3/99, 3:45 PM 9
10 4. Calculations Precision The HP 6S scientific calculator calculates answers to 12-digit accuracy , but rounds answers to 10 digits in the display . When it performs a calculation using the result of a previous calculation, it uses the sto red 12-digit value and not the 10-digit value displayed. Order of operations The HP 6S scientific calculator performs operations in the following order: º , à , à , à * , d , - & o , x , X Simple calculations Perform calculations in the same way that you write them on paper . 7.2Ã8.5 î 4.7Ã3.9 7.2*8.5-4.7*3.9= 42.87 4Ã8 4*8= 32. Specifying the order of calculations ( ) Use brackets to specify the order of calculations. Y ou can nest as many as six levels of brackets. Y ou do not need to enter the closing brackets. The calculator inserts them for you, although it does not display them. -5(4 3) 5Ã*(4 3= -35. Calculations English.PM6 3/3/99, 3:45 PM 10
11 Re-using arithmetic operations or ** etc 3 2.3 3 2.3= 5.3 6 2.3 6= 8.3 9 2.3 9= 11 . 3 4(3Ã6) 4**(3*6= 72. -5(3Ã6) 5Ã= -90. Using memory ´ m r ³ à ¡ f e Fraction arithmetic à Press to enter fractions. Press à after = to display the fraction as a decimal. In the display , a fraction is reduced to its lowest terms when you press a function command key (Ã,÷, ,-) or =. 4 5 / 6 à (3 1 2 / 3 ) ÷ 7 8 / 9 4Ã5Ã6*(3 1Ã2Ã3)d7Ã8Ã9= 2 à 61 à 71. à 2.86 Press the arithmetic operator key twice to re-use an arithmetic operation on a new number . Th e calculator stores the operation and applies it when you enter another number and press = . Store a calculation for re-use by enclosing it in brackets. Clear the stored arithmetic operation by pressing à . The HP 6S scientific calculator has one independent memory . M is displayed when there is a value in memory . Press à to clear the display or cancel the current calculation without clearing the memory . Press ´ to store the displayed value in memory . Press m to add the displayed value to the memory . Press r to retrieve the contents of memoryîto determine its value or include it in your calculation. Press I³ to display the contents of memory and replace it with the value that was displayed before the keys were pressed. Press ¡ to clear the display and the memory (solar model). Press fe to clear the display and the memory ( batt ery model). Calculations English.PM6 3/3/99, 3:45 PM 11
12 (1.5Ã10 7 ) î [(2.5Ã10 6 ) à 3 / 100 ] = 1.5¹7-2.5¹6*3Ã100= 149250000. 3 456 / 78 = 8 11 / 13 3Ã456Ã78 3 à 456 à 78. = 8à 11 à 13. I¬ Press these keys to switch between proper and improper fractions. 8 11 / 13 = 11 5 / 13 8 à 11 à 13. I¬ 11 5 à 13. I¬ 8 à 11 à 13. The answer to a calculation involving both fractions and decimals is displayed as a decimal. 41 / 52 à 78.9 41Ã52*78.9= 62.20961538 Percent age calculations I% Press to perform percentage calculations. 12% of 1500 1500*12I%= 180. 660 as a percentage of 880 660d880I%= 75. 2500 plus 15% 2500 15I% 375. = 2875. 25% discount on 3500 3500-25I% 875. = 2625. 26% of 2200; 26% of 3300; 26% of 3800; 2200**26I%= 572. 3300= 858. 3800= 988. $80 last week; $100 this week: what % is the new value of the old value? 100d80I%= 125. What % is 138gm to 150gm and 129gm to 150gm? 138dd150I%= 92. 129= 86. Calculations English.PM6 3/3/99, 3:45 PM 12
13 â 2 5. Other functions Converting minutes and seconds to decimal format à Press to convert minutes and seconds (sexagesimal figure) to decimal format. When you enter the sexagesimal figure, enter the degrees to the left of the decimal point, and minutes and seconds to the rightîthe first and second digits to the left of decimal point are minutes and the third and subsequent digits seconds. Ià Press to convert decimal format to sexagesimal format. 14 ° 25â² 36 â³ 14.2536à 14.42666667 Ià 14 ° 25 â² 36 â³ Conversion between angles, radians and grads Ià 45 ° = 0.785398163 rad = 50 grad 45Ià RAD 0.785398163 Ià GRAD 50. Ià DEG 45. T rigonometric functions sin ( Ï /6 rad) = RAD IPd6=s RAD 0.5 cos 63 ° 52â² 41â³ = DEG 63.5241à DEG 63.87805556 c DEG 0.440283084 t an (-35 grad) = GRAD 35Ãt GRAD -0.612800788 2 ⢠sin 45 ° x cos 65 ° = DEG 2*45s*65c= DEG 0.597672477 cot 30 ° = 1 /t an 30 ° = DEG 30tà DEG 1.732050808 sec ( Ï /3 rad) = cos ( Ï /3 rad) RAD IPd3=cà RAD 2. cosec 30 ° = sin 30 ° 30sà DEG 2. cos - RAD 2IÃÃd2=c RAD 0. 760244597 tan î1 0.6104 = DEG .6104IT DEG 31.399891 18 Ià 31 ° 23 â² 59.6 â³ Press ¯ to switch between RAD, DEG and GRAD 1 1 2 Other functions DEG English.PM6 3/3/99, 3:45 PM 13
14 Hyperbolic functions sinh 3.6 = 3.6ªs 18.28545536 tanh 2.5 = 2.5ªt 0.986614298 cosh 1.5 î sinh 1.5 = 1.5´ªc- M 2.352409615 rªs= M 0.22313016 sinh î1 30 = 30IªS 4.094622224 solve tanh 4x = 0.88 x = tan î1 = .88IªTd4= 0.343941914 Logarithmic functions log 1.23 (=log 10 1.23) = 1.23L 0.0899051 1 1 solve 4 x = 64 log 64 x = log 4 64Ld4L= 3. log 456 ÷ In 456 = 456´LdrÃ= M 0.434294481 10 0.4 5 ⢠e .3 = .4Ià 5*3ÃIÃ= 2.760821773 5.6 2.3 = 5.6Ã2.3= 52.58143837 123 1 / 7 (= 7 â 123) = 123IÃ7= 1.988647795 (78 î 23) -12 = (78-23)Ã12Ã= 1.3051 1 1829 -21 3 12 e 10 = 3Ã12 10IÃ= 553467.4658 Powers and root s â 2 â 3 x â 5 = 2Ià 3IÃ*5IÃ= 5.287196909 3 â 5 3 â -27 = 5Ià 27ÃIà -1.290024053 123 30 2 = 123 30º= 1023. 8! (=1 x 2 x 3 x î x 7 x 8 ) = 8Ià 40320 4 0.88 Other functions English.PM6 3/3/99, 3:45 PM 14
15 Miscellaneous functions 1.234 1.234 = I¼21.234 1.23 1.234= 2.47 I¼. 2.468 1 ÷ 3 1 ÷ 3 = I¼21d3 0.33 I½ 3.33-01 1d3= 6.67-01 I» 0.67 I¼. 0.666666666 123m x 456m = 56088m 123*456= 56088. = 56.088km I¾ 56.088 03 7.8g ÷ 96 = 0.08125g 7.8d96= 0.08125 = 81.25mg I¾ 81.25 - 03 Polar to rect angular coordinates conversions Formula: x = r ⢠cos θ y = r ⢠sin θ eg, find the value of x and y when the point P is shown as θ =60 and the length r=2 in the polar coordinates DEG 2I²60Ià 1. (x) I² 1.732050808 (y) I² 1. (x) Rect angular to polar coordinates conversions Formula: r = â x 2 y 2 θ = tan -1 y / x (-180 ° <θ ⥠180 ° ) eg, find the length r and the angle θ in radian when the point P is shown as x=1 and y= â 3 in the rect angular coordinates. RAD 1I²3IÃÃ= 2. (r) I² 1.047197551 ( θ in radian) I² 2. (r) Other functions English.PM6 3/3/99, 3:45 PM 15
16 Binary/oct al/decimal/hexadecimal conversions Conversion of 22 10 to binary . 22MÂ¥ BIN 101 10. Conversion of 22 10 to octal. M§ OCT 26. Conversion of 513 10 to binary . 513MÂ¥ E BIN 0. Conversion to binary mode generates an error if the result is greater than 10 digits. Conversion of 7FFFFFFF 16 to decimal. M¦7FFFFFFFM¤ 2147483647. Conversion of 123456 10 to octal. 123456M§ OCT 361 100. Conversion of 1 1001 10 2 to decimal. MÂ¥1100110M¤ 102. Binary/oct al/decimal/hexadecimal calculations M 101 1 1 2 1 1010 2 = 1 10001 2 ¦§ MÂ¥1011 1101= BIN 1 1000. ¥¤ 123 8 x ABC 16 =37AF4 16 M§123*M¦ABC= HEX 37AF4. =228084 10 M¤ 228084. 1F2D 16 î 100 10 =7881 10 M¦1F2D-M¤100 7881. =1EC9 16 M¦= HEX 1EC9. 6. Binary , oct al and hexadecimal values M ¦§ ¥¤ Use the M key to set the number base. When you use bases other than 10, you can only enter numbers valid for the baseîeg, in binary mode you can only enter 1 and 0 . M¦ sets the mode to hexadecimal. In hexadecimal mode, A to F keys are enabled. Note that b and d in hexadecimal mode are shown in lower case to distinguish them from numbers. M§ sets the mode to octal. MÂ¥ sets the mode to binary . M¤ sets the mode to decimal. Note: When using a number base other than 10, any fractional part is truncated. Binary, octal and hexadecimal values English.PM6 3/3/99, 3:45 PM 16
17 7654 8 ÷ 12 10 = 334.33î .10 M§7654dM¤12= 334.3333333 = 516 8 M§ OCT 516. Fractional part s of calculation results are truncated. 11 0 2 456 8 x78 10 ÷1A 16 MÂ¥110 M§456* =390 16 M¤78dM¦1A= HEX 390. =912 10 M¤ 912. Multiplication and division are given priority over addition and subtraction in mixed calculations. BC 16 x (14 10 69 10 =15604 10 =3CF4 16 M¦BC*(M¤14 69)= 15604. M¦ HEX 3CF4. Logical operations &o xX à Y ou can use the following logical operations to compare two numbers. When performing logical operations, keep the following points in mind: ⢠Y ou cannot use decimal-base numbers in logical operations. ⢠The calculator compares the binary versions of the numbers you enter. If the number is less than 10 digits long, the calculator fills values to the left of the number with 0sîeg, if you compare hexadecimal F1 to octal 4, the calculator compares 0000010001 to 0000000100. ⢠If you use one number with a logical operation, the calculator compares it to 0000000000. The logical operators work in the following way: 1. The operation compares the binary digits in the corresponding positions in each of the numbers. 2. The operation returns a binary digit corresponding to each position. 3. If you are using a base other than binary , the result is shown in the base of the last number you entered. The following logical operators are available: & returns a 1 for every position where there is a 1 in both numbers. o returns a 1 for every position where there is a 1 in either number . x returns a 1 for every position where there is a 1 in either number , but not both numbers. X returns a 1 for every position where there is the same digit in both numbers. à returns the diminished radix complement. Press these keys to perform the respective binary , octal, decimal and hexadecimal logical operations. Binary, octal and hexadecimal values English.PM6 3/3/99, 3:45 PM 17
18 19 16 AND 1A 16 = 18 16 M¦19&1A= HEX 18. 120 16 OR 1 101 2 = 12D 16 M¦ 120oMÂ¥1101= BIN 100101 101 . M¦ HEX 12d. 5 16 XOR 3 16 = 6 16 M¦5X3= HEX 6. 2A 16 XNOR 5D 16 = FFFFFFFF88 16 M¦2AX5D= HEX FFFFFFFF88 . 1A 16 AND 2F 16 = A 16 M¦1A&&2F= HEX A. NOT of 1010 2 MÂ¥10110à BIN 1 1 1 1 101001 . Radix complement IN Press to calculate and display the radix complement of the hexadecimal, octal or binary number currently displayedîie, 10000000000-the binary version of the number . Binary, octal and hexadecimal values English.PM6 3/3/99, 3:45 PM 18
19 7. Using st atistics M¿ Press to use statistics mode. Statistics mode allows you to enter data and apply the statistics functions to analyse the data. Entering a list of dat a items to analyse à Press after each data element. When you press à , the calculator displays the number of data elements entered. For example, to enter a list of data consisting of 5, 8 and -3, use the following keystrokes: 5 à 8 Ã3 à à T o enter the results of a calculation as a data item, perform the calculation as you would normally , then press à when the answer is displayed. Y ou can amend the data entered into the calculator: T o cancel the last entry you made, press à before you press à . Note that when you press à , 0 is displayed. Press In to display the number of data elements stored in the calculator . T o delete a data item you entered previously , enter the value again, then press Ià . Using st atistical functions on your dat a In Ãà Ãà à à Find the sample standard deviation of the data 5, 9 13 and 6. M¿5Ã9Ã13Ã6ÃIà SD 3.593976442 4, 1, 82, 59, 2, and 103 were entered, but 59 was entered by mistake. It should have been 58. T o fix the mistake, enter the wrong number , 59, and Ià , then enter the right number , 58, and à . Once you enter a list of data values you can use the following statistical functions: In The number of data elements entered Ià Sample standard deviation Ià Population standard deviation Ià Arithmetic mean Ià The sum of each data element Ià The sum of the data elements squared Using statistics English.PM6 3/3/99, 3:45 PM 19
20 8. Specifications Scientific functions/input range sinx / cosx / tanx |x|<4.5x10 10 degrees (<25x10 7 Ï rad,<5x10 10 grad sin -1 x / cos -1 x |x| ⥠1 tan -1 x |x|<10 100 sinhx / coshx |x| ⥠230.2585092 tanhx |x|<10 100 sinh -1 x |x|<5x10 99 cosh -1 x |x| ⥠x<5x10 99 tanh -1 x |x|<1 logx / Inx 10 -99 ⥠x<10 100 e x -10 100 <x ⥠230.2585092 10 x -10 100 <x<100 y x y>0 â 10 100 <x ⢠logy<100 y=0 âx>0 y<0 â x : integer or 1 / 2n 1 (n : integer) x â y y>0â xâ 0 : -10 100 < 1 / x ⢠logy<230.2582092 y=0 âx>0 y<0 â x : odd number or 1 / n (n : integer) â x0 ⥠x<10 100 x 2 |x|<10 50 3 â x |x|<10 100 1 / x |x|<10 100 (x â o) n! 0 ⥠x<69 (x: integer) REC â POL â x 2 y 2 <10 100 POL â REC | θ |<4.5x10 10 degrees (<25x10 7 rad, <5x10 10 grad) 0 ⥠r ⥠10 100 DMS â DEG |x | ⥠10 100 DEG â DMS |x | ⥠10 7 Ï 10 digits Binary Positive: 0 ⥠x ⥠1111111111 Negative: 1000000000 ⥠x⥠1111111111 Octal Positive: 0 ⥠x⥠3777777777 Negative: 4000000000 ⥠x⥠7777777777 Decimal Positive: 0 ⥠x⥠9999999999 Negative: -9999999999 ⥠x<0 Hexadecimal Positive: 0 ⥠x ⥠2540BE3FF Negative: FDABF41C01 ⥠x⥠FFFFFFFFFF Specifications English.PM6 3/3/99, 3:45 PM 20
21 Read-out ⢠Liquid crystal display suppressing unnecessary 0s (zeros). Power source ⢠Silicon solar cell (solar model only) ⢠Alkaline manganese battery (LR43)î1 battery for the solar model; 2 batteries for the non-solar model. Ambient T emperature range ⢠0° Cî40 ° C (32 ° Fî104 ° F). Dimensions ⢠127mmH x 72mmW x 8.5mmD (not including the wallet). Net weight 91g (including wallet). 9. Changing the battery · Replace the battery when: Replace the battery (alkaline manganese battery (LR43)î1 in the solar model and 2 in the non-solar model) when the display darkens under poor light condition, or disappears, and cannot be restored by pressing ¡ . · T o replace the battery: 1. Remove the four screws at the back of the calculator . Donât loose the screws . 2. Remove the back panel. 3. Remove the old battery . Lever it out with a sharp object like a pen. 4. Install the new battery with the sign at the uppermost. 5. Replace the back panel and the screws. 6. Check the display to make sure it is showing 0 in DEG mode. Changing the battery English.PM6 3/3/99, 3:45 PM 21
2 NOTICE This manual and any examples contained herein are provided as is and are subject to change without notice. Except to the extent prohibited by law , Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manual and specifically disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein. © Hewlett-Packard Company 1999. All rights reserved. REGULA T ORY INFORMA TION USA This calculator has been tested and found to comply with the limits for a Class B digital device, pursuant to part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This calculator generates, uses and can radiate radio frequency energy and may interfere with radio and television reception. In the unlikely event that this equipment does cause interference to radio or television reception, try the following: ⢠reorient or relocate the receiving antenna ⢠increase separation between the calculator and the receiver ⢠consult your dealer or an experienced radio/TV technician for help. CANADA This Class B digital apparatus complies with Canadian ICES-003. Cet appareil numérique de la classe B est conforme à la norme NMB-003. English.PM6 3/3/99, 3:45 PM 2
3 Contents 1. Keyboard 5 General keys 5 Memory keys 5 Special keys 5 Base-n keys 5 Function keys 6 Statistical keys 6 2. The display 7 Exponent displays 7 3. Basic functions 8 Entering numbers 8 Entering negative numbers 8 Entering exponential numbers 8 Arithmetic operator 8 Equals 8 Making corrections 9 Clearing errors 9 Fixing the number of decimal places displayed 9 Setting the display to scientific notation 9 4. Calculations 10 Precision 10 Order of operations 10 Simple calculations 10 Specifying the order of calculations 10 Re-using arithmetic operations 1 1 Using memory 1 1 Fraction arithmetic 1 1 Percentage calculations 12 5. Other functions 13 Converting minutes and seconds to decimal format 13 Conversion between angles, radians and grads 13 T rigonometric functions 13 Hyperbolic functions 14 Logarithmic functions 14 Powers and roots 14 Miscellaneous functions 15 Polar to rectangular coordinates conversions 15 Rectangular to polar coordinates conversions 15 English.PM6 3/3/99, 3:45 PM 3
4 6. Binary , octal and hexadecimal values 16 Binary/octal/decimal/hexadecimal conversions 16 Binary/octal/decimal/hexadecimal calculations 16 Logical operations 17 Radix complement 18 7 . Using statistics 1 9 Entering a list of data items to analyse 1 9 Using statistical functions on your data 19 8 . Specifications 2 0 9 . Changing the battery 2 1 English.PM6 3/3/99, 3:45 PM 4
5 1. Keyboard General keys Key Functions Page 0 to9 : . Data entry 8 -* Basic calculation 8 d= ¡ Reset the calculator 9 and clear the memory à Clear/clear error 9 à Change sign 8 Memory keys Key Functions Page r Retrieve data from the 11 independent memory ´ Store display data in 11 memory ³ Exchange of display data 11 and contents of memory m Add displayed data to 11 memory Special keys Key Functions Page I Inverse 7 M Mode 7 () Brackets (parentheses) 10 ¹ Exponent 8 P Pi 13 Key Functions Page Ãà Sexagesimal/decimal 13 notation conversion ¯ Mode of angle 13 DEG â RADâ GRADâ DEG à Angular conversion of data 13 DEG â RAD â GRAD â DEG ² Register exchange 11 à Clearing the last 9 entered digit ¼ Fix the number of digits 9 after the decimal point » Floating notation 9 ½ Scientific notation 9 ¾ Engineering notation 15 Base-n keys Key Functions Page ¤ Decimal 16 Â¥ Binary 16 ¦ Hexadecimal 16 § Octal 16 A to F Hexadecimal numbers only 16î18 & And 17 o Or 17 x Exclusive Or 17 X Exclusive Nor 17 à Not 17 N Negative 18 Keyboard English.PM6 3/3/99, 3:45 PM 5
6 Function keys K e y Functions Page s Sine 13 c Cosine 13 t T angent 13 S Arc sine 13 ¨ Arc cosine 13 T Arc tangent 13 ª Hyperbolic 14 L Common logarithm 14 à Common antilogarithm 14 à Natural logarithm 14 à Natural antilogarithm 14 à Square root 14 º Square 14 ì Fraction 12 à Cube root 14 à Reciprocal 12 à Factorial 14 K e y Functions Page à Power 8 à Root 14 à Rectangle to polar 15 à Polar to rectangular 15 % Percent 12 Statistical keys Key Functions Page ¿ Statistical data mode 19 à Data entry 19 à Data delete 19 à Sample standard deviation 19 à Population standard deviation 19 à Arithmetic mean 19 n Number of data 19 à Sum of value 19 à Sum of square value 19 Keyboard English.PM6 3/3/99, 3:45 PM 6
7 2. The display INV HYP BIN OCT HE X M E 1 2 . 5 4 3 Mantissa LCD Diagram The display shows input data, interim results and answers to calculations. The mantissa section displays up to 10 digits. The exponent section displays up to ± 99. Display Meaning Page -E- Indicates an error 9 INV I has been pressed to enable inverse key functions 9 M Indicates that data is stored in the memory 1 1 HYP ª has been pressed for hyperbolic functions 14 BIN, OCT , HEX BASE-N mode has been selected 1 6 SD Statistical mode has been selected 19 DEG, RAD, GRAD ¯ has been pressed to switch between the DEG, RAD and GRAD 13 angle types FIX (this does not display) The number of decimal places of a displayed value has been set 9,15 SCI (this does not display) Converts a displayed value to exponent display 9 ENG (this does not display) Converts a displayed value to exponent display of which the exponent 15 is a multiple of 3 and mantissa is between 0 to 999 FLO (this does not display) Convert a SCI or ENG form display to a normal display value 15 45 à 12 à 123 45 12 / 123 11 12. ° 3'45.6" Sexagesimal figure 12 ° 3'45.6" 13 Exponent displays The display can show calculation results only up to 10 digits long. When an intermediate value or a final result is longer than 10 digits, the calculator automatically switches over to exponential notation. V alues greater than 9,999,999,999 are always displayed exponentially . The Display English.PM6 3/3/99, 3:45 PM 7
8 3. Basic functions Entering numbers 123 etc . Entering negative numbers à Press after a number to make it negative. 5.08à -5.08 Entering exponential numbers ¹ Press to enter an exponential number . 3.08Ã10 9 3.08¹9 3.08 09 Arithmetic operator -* dà 4*d - 5 9. Equals = Press to complete your calculation and display a result. If you press = more than once without entering a number , the calculator performs the last arithmetic operation on the value displayed. 4Ã8 4*8= 32. 4*8== 256. Press the number keys to enter numbers. Press . for a decimal point. Press to perform an arithmetic operation on the value displayed. Y ou must enter a number after the arithmetic operator . If you press more than one arithmetic operator in sequence, the calculator only performs the last operation (the last key pressed). Basic functions English.PM6 3/3/99, 3:45 PM 8
9 Making corrections à Press to delete the last number entered. à Press to remove the displayed value, but retain the calculation being performed. Press after the arithmetic operator to cancel the entire calculation. 5 5 5 6Ã5= 20. 5 5 5 Ã= 0. Clearing errors à Press to clear an error (indicated by î-E-î in the display)îeg, an overflow errorîand retain data in the memory . ¡ Press to reset the calculator and clear the memory (solar model only). Fixing the number of decimal places displayed I¼ Press after your arithmetic operation, or after you press ¡ , to set the number of decimal 2 places displayed (the number you press is the number of decimal places you want to display). The calculator rounds the number in the display but maintains full precision internally . I Press to reset the floating decimal point. ¼. Setting the display to scientific not ation I Press to set the display to scientific notation and express the number as a power ofî 10îeg, ½ .0043 is displayed as 4.3. -03 to represent 4.3Ã10 -3 . I Press to reset the display to the floating format. » Basic functions English.PM6 3/3/99, 3:45 PM 9
10 4. Calculations Precision The HP 6S scientific calculator calculates answers to 12-digit accuracy , but rounds answers to 10 digits in the display . When it performs a calculation using the result of a previous calculation, it uses the sto red 12-digit value and not the 10-digit value displayed. Order of operations The HP 6S scientific calculator performs operations in the following order: º , à , à , à * , d , - & o , x , X Simple calculations Perform calculations in the same way that you write them on paper . 7.2Ã8.5 î 4.7Ã3.9 7.2*8.5-4.7*3.9= 42.87 4Ã8 4*8= 32. Specifying the order of calculations ( ) Use brackets to specify the order of calculations. Y ou can nest as many as six levels of brackets. Y ou do not need to enter the closing brackets. The calculator inserts them for you, although it does not display them. -5(4 3) 5Ã*(4 3= -35. Calculations English.PM6 3/3/99, 3:45 PM 10
11 Re-using arithmetic operations or ** etc 3 2.3 3 2.3= 5.3 6 2.3 6= 8.3 9 2.3 9= 11 . 3 4(3Ã6) 4**(3*6= 72. -5(3Ã6) 5Ã= -90. Using memory ´ m r ³ à ¡ f e Fraction arithmetic à Press to enter fractions. Press à after = to display the fraction as a decimal. In the display , a fraction is reduced to its lowest terms when you press a function command key (Ã,÷, ,-) or =. 4 5 / 6 à (3 1 2 / 3 ) ÷ 7 8 / 9 4Ã5Ã6*(3 1Ã2Ã3)d7Ã8Ã9= 2 à 61 à 71. à 2.86 Press the arithmetic operator key twice to re-use an arithmetic operation on a new number . Th e calculator stores the operation and applies it when you enter another number and press = . Store a calculation for re-use by enclosing it in brackets. Clear the stored arithmetic operation by pressing à . The HP 6S scientific calculator has one independent memory . M is displayed when there is a value in memory . Press à to clear the display or cancel the current calculation without clearing the memory . Press ´ to store the displayed value in memory . Press m to add the displayed value to the memory . Press r to retrieve the contents of memoryîto determine its value or include it in your calculation. Press I³ to display the contents of memory and replace it with the value that was displayed before the keys were pressed. Press ¡ to clear the display and the memory (solar model). Press fe to clear the display and the memory ( batt ery model). Calculations English.PM6 3/3/99, 3:45 PM 11
12 (1.5Ã10 7 ) î [(2.5Ã10 6 ) à 3 / 100 ] = 1.5¹7-2.5¹6*3Ã100= 149250000. 3 456 / 78 = 8 11 / 13 3Ã456Ã78 3 à 456 à 78. = 8à 11 à 13. I¬ Press these keys to switch between proper and improper fractions. 8 11 / 13 = 11 5 / 13 8 à 11 à 13. I¬ 11 5 à 13. I¬ 8 à 11 à 13. The answer to a calculation involving both fractions and decimals is displayed as a decimal. 41 / 52 à 78.9 41Ã52*78.9= 62.20961538 Percent age calculations I% Press to perform percentage calculations. 12% of 1500 1500*12I%= 180. 660 as a percentage of 880 660d880I%= 75. 2500 plus 15% 2500 15I% 375. = 2875. 25% discount on 3500 3500-25I% 875. = 2625. 26% of 2200; 26% of 3300; 26% of 3800; 2200**26I%= 572. 3300= 858. 3800= 988. $80 last week; $100 this week: what % is the new value of the old value? 100d80I%= 125. What % is 138gm to 150gm and 129gm to 150gm? 138dd150I%= 92. 129= 86. Calculations English.PM6 3/3/99, 3:45 PM 12
13 â 2 5. Other functions Converting minutes and seconds to decimal format à Press to convert minutes and seconds (sexagesimal figure) to decimal format. When you enter the sexagesimal figure, enter the degrees to the left of the decimal point, and minutes and seconds to the rightîthe first and second digits to the left of decimal point are minutes and the third and subsequent digits seconds. Ià Press to convert decimal format to sexagesimal format. 14 ° 25â² 36 â³ 14.2536à 14.42666667 Ià 14 ° 25 â² 36 â³ Conversion between angles, radians and grads Ià 45 ° = 0.785398163 rad = 50 grad 45Ià RAD 0.785398163 Ià GRAD 50. Ià DEG 45. T rigonometric functions sin ( Ï /6 rad) = RAD IPd6=s RAD 0.5 cos 63 ° 52â² 41â³ = DEG 63.5241à DEG 63.87805556 c DEG 0.440283084 t an (-35 grad) = GRAD 35Ãt GRAD -0.612800788 2 ⢠sin 45 ° x cos 65 ° = DEG 2*45s*65c= DEG 0.597672477 cot 30 ° = 1 /t an 30 ° = DEG 30tà DEG 1.732050808 sec ( Ï /3 rad) = cos ( Ï /3 rad) RAD IPd3=cà RAD 2. cosec 30 ° = sin 30 ° 30sà DEG 2. cos - RAD 2IÃÃd2=c RAD 0. 760244597 tan î1 0.6104 = DEG .6104IT DEG 31.399891 18 Ià 31 ° 23 â² 59.6 â³ Press ¯ to switch between RAD, DEG and GRAD 1 1 2 Other functions DEG English.PM6 3/3/99, 3:45 PM 13
14 Hyperbolic functions sinh 3.6 = 3.6ªs 18.28545536 tanh 2.5 = 2.5ªt 0.986614298 cosh 1.5 î sinh 1.5 = 1.5´ªc- M 2.352409615 rªs= M 0.22313016 sinh î1 30 = 30IªS 4.094622224 solve tanh 4x = 0.88 x = tan î1 = .88IªTd4= 0.343941914 Logarithmic functions log 1.23 (=log 10 1.23) = 1.23L 0.0899051 1 1 solve 4 x = 64 log 64 x = log 4 64Ld4L= 3. log 456 ÷ In 456 = 456´LdrÃ= M 0.434294481 10 0.4 5 ⢠e .3 = .4Ià 5*3ÃIÃ= 2.760821773 5.6 2.3 = 5.6Ã2.3= 52.58143837 123 1 / 7 (= 7 â 123) = 123IÃ7= 1.988647795 (78 î 23) -12 = (78-23)Ã12Ã= 1.3051 1 1829 -21 3 12 e 10 = 3Ã12 10IÃ= 553467.4658 Powers and root s â 2 â 3 x â 5 = 2Ià 3IÃ*5IÃ= 5.287196909 3 â 5 3 â -27 = 5Ià 27ÃIà -1.290024053 123 30 2 = 123 30º= 1023. 8! (=1 x 2 x 3 x î x 7 x 8 ) = 8Ià 40320 4 0.88 Other functions English.PM6 3/3/99, 3:45 PM 14
15 Miscellaneous functions 1.234 1.234 = I¼21.234 1.23 1.234= 2.47 I¼. 2.468 1 ÷ 3 1 ÷ 3 = I¼21d3 0.33 I½ 3.33-01 1d3= 6.67-01 I» 0.67 I¼. 0.666666666 123m x 456m = 56088m 123*456= 56088. = 56.088km I¾ 56.088 03 7.8g ÷ 96 = 0.08125g 7.8d96= 0.08125 = 81.25mg I¾ 81.25 - 03 Polar to rect angular coordinates conversions Formula: x = r ⢠cos θ y = r ⢠sin θ eg, find the value of x and y when the point P is shown as θ =60 and the length r=2 in the polar coordinates DEG 2I²60Ià 1. (x) I² 1.732050808 (y) I² 1. (x) Rect angular to polar coordinates conversions Formula: r = â x 2 y 2 θ = tan -1 y / x (-180 ° <θ ⥠180 ° ) eg, find the length r and the angle θ in radian when the point P is shown as x=1 and y= â 3 in the rect angular coordinates. RAD 1I²3IÃÃ= 2. (r) I² 1.047197551 ( θ in radian) I² 2. (r) Other functions English.PM6 3/3/99, 3:45 PM 15
16 Binary/oct al/decimal/hexadecimal conversions Conversion of 22 10 to binary . 22MÂ¥ BIN 101 10. Conversion of 22 10 to octal. M§ OCT 26. Conversion of 513 10 to binary . 513MÂ¥ E BIN 0. Conversion to binary mode generates an error if the result is greater than 10 digits. Conversion of 7FFFFFFF 16 to decimal. M¦7FFFFFFFM¤ 2147483647. Conversion of 123456 10 to octal. 123456M§ OCT 361 100. Conversion of 1 1001 10 2 to decimal. MÂ¥1100110M¤ 102. Binary/oct al/decimal/hexadecimal calculations M 101 1 1 2 1 1010 2 = 1 10001 2 ¦§ MÂ¥1011 1101= BIN 1 1000. ¥¤ 123 8 x ABC 16 =37AF4 16 M§123*M¦ABC= HEX 37AF4. =228084 10 M¤ 228084. 1F2D 16 î 100 10 =7881 10 M¦1F2D-M¤100 7881. =1EC9 16 M¦= HEX 1EC9. 6. Binary , oct al and hexadecimal values M ¦§ ¥¤ Use the M key to set the number base. When you use bases other than 10, you can only enter numbers valid for the baseîeg, in binary mode you can only enter 1 and 0 . M¦ sets the mode to hexadecimal. In hexadecimal mode, A to F keys are enabled. Note that b and d in hexadecimal mode are shown in lower case to distinguish them from numbers. M§ sets the mode to octal. MÂ¥ sets the mode to binary . M¤ sets the mode to decimal. Note: When using a number base other than 10, any fractional part is truncated. Binary, octal and hexadecimal values English.PM6 3/3/99, 3:45 PM 16
17 7654 8 ÷ 12 10 = 334.33î .10 M§7654dM¤12= 334.3333333 = 516 8 M§ OCT 516. Fractional part s of calculation results are truncated. 11 0 2 456 8 x78 10 ÷1A 16 MÂ¥110 M§456* =390 16 M¤78dM¦1A= HEX 390. =912 10 M¤ 912. Multiplication and division are given priority over addition and subtraction in mixed calculations. BC 16 x (14 10 69 10 =15604 10 =3CF4 16 M¦BC*(M¤14 69)= 15604. M¦ HEX 3CF4. Logical operations &o xX à Y ou can use the following logical operations to compare two numbers. When performing logical operations, keep the following points in mind: ⢠Y ou cannot use decimal-base numbers in logical operations. ⢠The calculator compares the binary versions of the numbers you enter. If the number is less than 10 digits long, the calculator fills values to the left of the number with 0sîeg, if you compare hexadecimal F1 to octal 4, the calculator compares 0000010001 to 0000000100. ⢠If you use one number with a logical operation, the calculator compares it to 0000000000. The logical operators work in the following way: 1. The operation compares the binary digits in the corresponding positions in each of the numbers. 2. The operation returns a binary digit corresponding to each position. 3. If you are using a base other than binary , the result is shown in the base of the last number you entered. The following logical operators are available: & returns a 1 for every position where there is a 1 in both numbers. o returns a 1 for every position where there is a 1 in either number . x returns a 1 for every position where there is a 1 in either number , but not both numbers. X returns a 1 for every position where there is the same digit in both numbers. à returns the diminished radix complement. Press these keys to perform the respective binary , octal, decimal and hexadecimal logical operations. Binary, octal and hexadecimal values English.PM6 3/3/99, 3:45 PM 17
18 19 16 AND 1A 16 = 18 16 M¦19&1A= HEX 18. 120 16 OR 1 101 2 = 12D 16 M¦ 120oMÂ¥1101= BIN 100101 101 . M¦ HEX 12d. 5 16 XOR 3 16 = 6 16 M¦5X3= HEX 6. 2A 16 XNOR 5D 16 = FFFFFFFF88 16 M¦2AX5D= HEX FFFFFFFF88 . 1A 16 AND 2F 16 = A 16 M¦1A&&2F= HEX A. NOT of 1010 2 MÂ¥10110à BIN 1 1 1 1 101001 . Radix complement IN Press to calculate and display the radix complement of the hexadecimal, octal or binary number currently displayedîie, 10000000000-the binary version of the number . Binary, octal and hexadecimal values English.PM6 3/3/99, 3:45 PM 18
19 7. Using st atistics M¿ Press to use statistics mode. Statistics mode allows you to enter data and apply the statistics functions to analyse the data. Entering a list of dat a items to analyse à Press after each data element. When you press à , the calculator displays the number of data elements entered. For example, to enter a list of data consisting of 5, 8 and -3, use the following keystrokes: 5 à 8 Ã3 à à T o enter the results of a calculation as a data item, perform the calculation as you would normally , then press à when the answer is displayed. Y ou can amend the data entered into the calculator: T o cancel the last entry you made, press à before you press à . Note that when you press à , 0 is displayed. Press In to display the number of data elements stored in the calculator . T o delete a data item you entered previously , enter the value again, then press Ià . Using st atistical functions on your dat a In Ãà Ãà à à Find the sample standard deviation of the data 5, 9 13 and 6. M¿5Ã9Ã13Ã6ÃIà SD 3.593976442 4, 1, 82, 59, 2, and 103 were entered, but 59 was entered by mistake. It should have been 58. T o fix the mistake, enter the wrong number , 59, and Ià , then enter the right number , 58, and à . Once you enter a list of data values you can use the following statistical functions: In The number of data elements entered Ià Sample standard deviation Ià Population standard deviation Ià Arithmetic mean Ià The sum of each data element Ià The sum of the data elements squared Using statistics English.PM6 3/3/99, 3:45 PM 19
20 8. Specifications Scientific functions/input range sinx / cosx / tanx |x|<4.5x10 10 degrees (<25x10 7 Ï rad,<5x10 10 grad sin -1 x / cos -1 x |x| ⥠1 tan -1 x |x|<10 100 sinhx / coshx |x| ⥠230.2585092 tanhx |x|<10 100 sinh -1 x |x|<5x10 99 cosh -1 x |x| ⥠x<5x10 99 tanh -1 x |x|<1 logx / Inx 10 -99 ⥠x<10 100 e x -10 100 <x ⥠230.2585092 10 x -10 100 <x<100 y x y>0 â 10 100 <x ⢠logy<100 y=0 âx>0 y<0 â x : integer or 1 / 2n 1 (n : integer) x â y y>0â xâ 0 : -10 100 < 1 / x ⢠logy<230.2582092 y=0 âx>0 y<0 â x : odd number or 1 / n (n : integer) â x0 ⥠x<10 100 x 2 |x|<10 50 3 â x |x|<10 100 1 / x |x|<10 100 (x â o) n! 0 ⥠x<69 (x: integer) REC â POL â x 2 y 2 <10 100 POL â REC | θ |<4.5x10 10 degrees (<25x10 7 rad, <5x10 10 grad) 0 ⥠r ⥠10 100 DMS â DEG |x | ⥠10 100 DEG â DMS |x | ⥠10 7 Ï 10 digits Binary Positive: 0 ⥠x ⥠1111111111 Negative: 1000000000 ⥠x⥠1111111111 Octal Positive: 0 ⥠x⥠3777777777 Negative: 4000000000 ⥠x⥠7777777777 Decimal Positive: 0 ⥠x⥠9999999999 Negative: -9999999999 ⥠x<0 Hexadecimal Positive: 0 ⥠x ⥠2540BE3FF Negative: FDABF41C01 ⥠x⥠FFFFFFFFFF Specifications English.PM6 3/3/99, 3:45 PM 20
21 Read-out ⢠Liquid crystal display suppressing unnecessary 0s (zeros). Power source ⢠Silicon solar cell (solar model only) ⢠Alkaline manganese battery (LR43)î1 battery for the solar model; 2 batteries for the non-solar model. Ambient T emperature range ⢠0° Cî40 ° C (32 ° Fî104 ° F). Dimensions ⢠127mmH x 72mmW x 8.5mmD (not including the wallet). Net weight 91g (including wallet). 9. Changing the battery · Replace the battery when: Replace the battery (alkaline manganese battery (LR43)î1 in the solar model and 2 in the non-solar model) when the display darkens under poor light condition, or disappears, and cannot be restored by pressing ¡ . · T o replace the battery: 1. Remove the four screws at the back of the calculator . Donât loose the screws . 2. Remove the back panel. 3. Remove the old battery . Lever it out with a sharp object like a pen. 4. Install the new battery with the sign at the uppermost. 5. Replace the back panel and the screws. 6. Check the display to make sure it is showing 0 in DEG mode. Changing the battery English.PM6 3/3/99, 3:45 PM 21