HP 41/DM41L and TI-60X: Exponentiation of Large Numbers
But Why a Program when we have Button?
This is true. What this program does is allow for calculation of y^x when results in answers greater than 9.999999999 * 10^9. The number is broken up into the form:
mantissa * 10^exponent
Let n = y^x. Then:
n = y^x
Taking the logarithm of both sides:
log n = log (y^x)
log n = x log y
A number can be split into its fractional and integer part:
log n = frac(x log y) + int(x log y)
Take the antilog of both sides:
n = 10^( frac(x log y) + int(x log y) )
n = 10^( frac(x log y) ) * 10^( int(x log y) )
where
mantissa = 10^( frac(x log y) )
exponent = int(x log y)
HP 41/DM 41L Program BIGPOW
Input:
Y stack: y
X stack: x
Output:
Y: mantissa (shown first)
X: exponent
01 LBL T^BIGPOW
02 X<>Y
03 LOG
04 *
05 ENTER↑
06 FRC
07 10↑X
08 STOP
09 X<>Y
10 INT
11 RTN
TI-60 Program: Big Powers
Input:
Store y in R1 and x in R2
Output:
R1 = mantissa (shown first), R2 = exponent
(Step, Key Number, Key)
00, 71, RCL
01, 02, 2
02, 65, *
03, 71, RCL
04, 01, 1
05, 43, log
06, 95, =
07, 61, STO
08, 02, 2
09, 78, Frac
10, 12, INV
11, 43, log
12, 61, STO
13, 01, 1
14, 13, R/S
15, 71, RCL
16, 02, 2
17, 79, Intg
18, 13, R/S
19, 22, RST
Examples
Example 1: 25^76. y = 25, x = 76
Result:
Mantissa = 1.75162308
Exponent = 106
25^76 ≈ 1.75162308 * 10^106
Example 2: 78^55.25, y = 78, x = 55.25
Result:
Mantissa = 3.453240284
Exponent = 104
78^55.25 ≈ 3.543240284 * 10^104
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
But Why a Program when we have Button?
This is true. What this program does is allow for calculation of y^x when results in answers greater than 9.999999999 * 10^9. The number is broken up into the form:
mantissa * 10^exponent
Let n = y^x. Then:
n = y^x
Taking the logarithm of both sides:
log n = log (y^x)
log n = x log y
A number can be split into its fractional and integer part:
log n = frac(x log y) + int(x log y)
Take the antilog of both sides:
n = 10^( frac(x log y) + int(x log y) )
n = 10^( frac(x log y) ) * 10^( int(x log y) )
where
mantissa = 10^( frac(x log y) )
exponent = int(x log y)
HP 41/DM 41L Program BIGPOW
Input:
Y stack: y
X stack: x
Output:
Y: mantissa (shown first)
X: exponent
01 LBL T^BIGPOW
02 X<>Y
03 LOG
04 *
05 ENTER↑
06 FRC
07 10↑X
08 STOP
09 X<>Y
10 INT
11 RTN
TI-60 Program: Big Powers
Input:
Store y in R1 and x in R2
Output:
R1 = mantissa (shown first), R2 = exponent
(Step, Key Number, Key)
00, 71, RCL
01, 02, 2
02, 65, *
03, 71, RCL
04, 01, 1
05, 43, log
06, 95, =
07, 61, STO
08, 02, 2
09, 78, Frac
10, 12, INV
11, 43, log
12, 61, STO
13, 01, 1
14, 13, R/S
15, 71, RCL
16, 02, 2
17, 79, Intg
18, 13, R/S
19, 22, RST
Examples
Example 1: 25^76. y = 25, x = 76
Result:
Mantissa = 1.75162308
Exponent = 106
25^76 ≈ 1.75162308 * 10^106
Example 2: 78^55.25, y = 78, x = 55.25
Result:
Mantissa = 3.453240284
Exponent = 104
78^55.25 ≈ 3.543240284 * 10^104
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.