RPN: HP 15C and DM32: Integer Length and Digit Extraction

RPN: HP 15C and DM32: Integer Length and Digit Extraction (up to 99,999,999)

The following programs are utilities for positive integers:

(1) Integer Length: how many digits in a positive integer

(2) Digit Extraction: Get the nth digit of a positive integer

Note:  Do not use more than 8 digits (integers up to 99,999,999).   Beyond this, the program may return inaccurate answers.  

Thanks to J-F Garnier for pointing out the limitation of the programs.  

Integer Length

Find the number of digits of a positive integer. The integer is decimal base (base 10).

For a positive integer n, the number of the digits can be easily found by the formula:

L = int(log(x)) + 1

DM32, HP 32S, HP 32SII Code

L01 LBL L

L02 LOG

L03 IP

L04 1

L05 +

L06 RTN

HP 15C, DM15 Code

001	42, 21, 11	LBL A
002	43, 13	LOG
003	43, 44	INT
004	1	1
005	40	+
006	43, 32	RTN

The program finds the number of digits in the positive integer in the X stack.

Examples:

X = 436782; Length: 6

X = 5195008; Length: 7

X = 23156956; Length: 8

Digit Extraction

Extract the nth digit of a positive integer. Digit positions go from left to right. For example: for the integer 4582, the 1^st digit is 4, the 2^nd digit is 5, 3^rd digit is 8, and 4^th digit is 2.

Steps that this program follows:

Step 1: Find the length of the positive integer. L = int(log(x)) + 1.

Step 2: Divide X by 10^(L – n + 1). D = X / (10^(L – n + 1))

Step 3: Extract the fractional part. D = frac(D)

Step 4: Multiple the result by 10 and extract the integer part. D = int(10 * D)

Setting up the stack:

Y: integer

X: nth digit to extract

Variables Used:

DM32, HP 32S, HP 32S II	HP 15C, DM15
X	R1
N	R2
L	R3

DM32, HP 32S, HP 32SII Code

E01 LBL E

E02 STO N

E03 R↓

E04 STO X

E05 LOG

E06 IP

E07 1

E08 +

E09 STO L

E10 RCL X

E11 RCL L

E12 RCL- N

E13 1

E14 +

E15 10^x

E16 ÷

E17 FP

E18 10

E19 ×

E20 IP

E21 RTN

HP 15C, DM15 Code

001	42, 21, 12	LBL B
002	44, 2	STO 2
003	33	R↓
004	44, 1	STO 1
005	43, 13	LOG
006	43, 44	INT
007	1	1
008	40	+
009	44, 3	STO 3
010	45, 1	RCL 1
011	45, 3	RCL 3
012	45, 30, 2	RCL- 2
013	1	1
014	40	+
015	13	10^x
016	10	÷
017	42, 44	FRAC
018	1	1
019	0	0
020	20	×
021	43, 44	INT
022	43, 32	RTN

Examples

Integers	Length	2nd Digit	4th Digit	5th Digit
436782	6	3	7	8
5195008	7	1	5	0
23156956	8	3	5	6

Eddie

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