(15C) Decimal to x/16

[Dwight Sturrock]

HP 15c x/16

Program to convert decimal fraction to a fraction readable on a tape measure:

Registers:
STO 0- ORIGINAL NUMBER
STO 1- NUMERATOR
STO 2- DENOMINATOR

Code:

01 LBL A
02 STO 0
03 FRAC      //Creates numerator x as a fraction
             //with 16 as denominator: x/16
04 1         //Use 32 ON steps 04-05 if you want 32nds
05 6
06 STO 2
07 *
08 FIX 0
09 RND
10 FIX 3
11 INT
12 STO 1
13 LBL 7     //Can fraction be reduced?
14 2
15 /
16 FRAC
17 TEST 0     //Same as X#0
18 GTO 8     //If fraction can't be reduced,
             //go to formatting subroutine
19 RCL 2     //Reduce fraction
20 2
21 /
22 STO 2
23 RCL 1
24 2
25 /
26 STO 1
27 GTO 7     //Try again
28 LBL 8     //Formatting subroutine
29 RCL 0     //Original number will be left in y register
30 RCL 1     //The next 7 steps put the fraction
            //into the format Num.Deno:
31 RCL 2     //For Example, 1/16 will display
            //as 1.16, 5/8 as 5.08
32 .
33 0
34 1
35 *
36 +
37 RTN

[Thomas Klemm]

That's a nice program. Here's a variant that is a little shorter and uses only one register:

Code:

001-42,21,11    LBL A
002-    44 0    STO 0
003-   42 44    FRAC
004-      48    .
005-       5    5
006-      36    ENTER
007-      36    ENTER
008-   43 33    R^
009-       1    1
010-       6    6
011-      20    *
012-      40    +
013-   43 44    INT
014-      48    .
015-       1    1
016-       6    6
017-      40    +
018-42,21, 0    LBL 0
019-      20    *
020-   42 44    FRAC
021-43,30, 7    TEST 7 ; x>y
022-    22 1    GTO 1
023-   43 35    CLx
024-   43 36    LSTx
025-    22 0    GTO 0
026-42,21, 1    LBL 1
027-    45 0    RCL 0
028-   43 36    LSTx
029-      36    ENTER
030-      40    +
031-   43 32    RTN

The numerator and denominator are merged into a single number nn.dd. Thus we can divide both by 2 with a single instruction.
The display settings aren't changed since the function INT(x + 0.5) is used to round a number.
The stack is filled with 0.5 in lines 4-7 because this number can be used often.
Personally I dislike that 16 occurs twice but I couldn't come up with a better solution. Maybe somebody else can?

Kind regards
Thomas

[Dwight Sturrock]

Elegant, Thomas, and a bit faster.

I had a version for the 42S and I ported it quickly to the 15C years ago without much thought. It is a program I used on a daily basis in my work for many years.