From: Mike Mansheim of Graco, Inc.
/*
- based on the 16 bit to 5 digit conversion written by John Payson
& explained by Scott Dattalo
- this version adds the extra bit so that the 5 digit display can
read to 99,999
- want to express the b_i's in terms of the a_i's for the equations:
N = a4*16^4 + a3*16^3 + a2*16^2 + a1*16 + a0
N = b4*10^4 + b3*10^3 + b2*10^2 + b1*10 + b0
the solution coded below:
b0 = a0 - (4 * (a4 + a3 + a2 + a1)) - 20
b1 = (4 * a4) + (6 * a2) + (2 * a1) - 198
b2 = (5 * a4) + a3 + (2 * a2) - 140
b3 = (5 * a4) + (4 * a3) - 144
b4 = (6 * a4) + 16
- written in CCS C
- since ram was plentiful, I used a 3 byte number - only one bit
of the extra byte is actually required. I also used three bytes
of scratchpad ram to increase the efficiency of the compiled code.
The equations can be coded in C exactly as shown above, but that
doesn't take advantage of common terms & progressive multiplies.
- even with just the one extra bit, the incoming number can exceed
99,999, so it needs to be checked. This code doesn't show that.
- CCS C is limited to 16 bit as the largest integer data type. To
use a 24 bit number, I use an array to make sure the bytes are
consecutive. This function operates on the array as a global,
because I think that is more efficient than passing arrays to
the function.
- the code could be quite a bit smaller - in John's original, the
portion of the code that isolated the nibbles and calculated the
digits took 32 instructions. If I code that solution in C, using
two scratchpad bytes to improve things, it compiles to 64 instructions.
This version compiles to 85 instructions, so I'm sure an asm whiz
could show quite an improvement. The C version is still much faster
than the the original way I did this, and is adequate for what I need.
*/
unsigned int TenK, Thou, Hund, Tens, Ones;
unsigned int num[3];
void BIN2DEC(void)
{
// operates on global variables:
// set num[0]-[3] (lo-hi) before calling
// returns with TenK...Ones set from 0-9
unsigned int a0, a1, a2, a3, a4;
unsigned int t1, t2, t3; // scratchpad variables
// isolate the 4 bit nibbles
// for the purposes of this routine, a4 can be only 0 or 1
a4 = num[2];
a3 = num[1] / 16;
a2 = num[1] & 0b00001111;
a1 = num[0] / 16;
a0 = num[0] & 0b00001111;
// calculate the decimal digits (the b_i's are expressed here
// as TenK...Ones, as in the original)
// all are negative, except TenK
t1 = 4 * a4;
Ones = a0 - t1 - 20;
t2 = 2 * a1;
Tens = t1 + t2 - 198;
t3 = 2 * a2;
Hund = a3 + t3 - 140;
t3 = t3 * 2; // now = 4 * a2
t2 = t2 * 2; // now = 4 * a1
Ones = Ones - t3 - t2;
t3 = t3 + a2 + a2; // now = 6 * a2
Tens = Tens + t3; // Tens done
t1 = t1 + a4; // now = 5 * a4
Hund = Hund + t1;
t3 = 4 * a3;
Thou = t1 + t3 - 144; // Thou done
Ones = Ones - t3; // Ones done
TenK = t1 + a4 + 16; // Tenk done
// "normalize" the digits - this asm code was
// copied directly from the original
#asm
movlw 0x0A
Lb1:
addwf Ones,f
decf Tens,f
btfss 3,0
goto Lb1
Lb2:
addwf Tens,f
decf Hund,f
btfss 3,0
goto Lb2
Lb3:
addwf Hund,f
decf Thou,f
btfss 3,0
goto Lb3
Lb4:
addwf Thou,f
decf TenK,f
btfss 3,0
goto Lb4
#endasm
}
anhalt@zoominternet.net I tweaked Mike Mansheim's algorithm a little and would like to offer this code:
PICLIST Submission
17BIN2BCD
;February 6, 2018 ;John Anhalt ;41 Tcy to Normalize ;Enhanced mid-range PIC16F1829 ;"#" marks final polynomial for each BCD cblock 0x20 binU binH binL ones tens hund thou tenK endc org 0x0000 nop bra Start Start DoA2 movf binH,w andlw 0x0F ;w=a2 movwf ones ;ones=a2 movwf tens ;tens=a2 lslf WREG ;w=2a2 addlw 0xC7 ;-57 movwf hund ;hund=2a2-57 addlw 0xF9 ;-7 -57= -64 addwf tens,f ;tens=3a2-64 DoA4 movf binU,w addwf ones,f ;ones=a4+a2 addwf hund,f ;hund=a4+2a2-57 movwf thou ;thou=a4 lslf WREG ;w=2a4 movwf tenK ;tenK=2a4 addwf tens,f ;tens=2a4+3a2-64 lslf WREG ;w=4a4 addwf hund,f ;hund=5a4+2a2-57 addwf thou,f ;thou=5a4 addlw 8 ;w=4a4+8 addwf tenK,f ;tenK=6a4+8 # DoA3 swapf binH,w andlw 0x0F ;w=a3 addwf ones,f ;ones=a4+a3+a2 addwf hund,f ;hund=5a4+a3+2a2-57 # lslf WREG ;w=2a3 lslf WREG ;w=4a3 addlw 0xB7 ;-73 addwf thou,f ;thou=5a4+4a3-73 # DoA1 ;same as Payson/Dattalo, binL preserved swapf binL,w andlw 0x0F ;w=a1 addwf tens,f ;tens=2a4+3a2+a1-64 addlw 4 ;see: Payson/Dattalo explanation addwf ones ;ones=a4+a3+a2+a1+4 lslf tens,f ;tens=4a4+6a2+2a1-128,C is set # rlf ones,f ;moves C into ones comf ones,f rlf ones,f ;w/ carry ones is complement 2 negated movf binL,w andlw 0x0F ;w=a0 addwf ones,f ;ones=a0-4(a4+a3+a2+a1)-20 # Normalize movlw 0x0A Lb1 addwf ones,f decf tens,f btfss STATUS,0 bra Lb1 Lb2 addwf tens,f decf hund,f btfss STATUS,0 bra Lb2 Lb3 addwf hund,f decf thou,f btfss STATUS,0 bra Lb3 Lb4 addwf thou,f decf tenK,f btfss STATUS,0 bra Lb4 bra Done DoneExplanation (Based on Mike Mansheim)
Consider a 17-bit binary (N)= a4(2^16) +a3(2^12) + a2(2^8) + a1(2^4) +a0(2^0) where a_i is a 4-bit nibble.
A set of polynomials can be derived where b_i is the BCD digit:
b0(ones) = a0-4(a4+a3+a2+a1)
b1 (tens) = 4a4+6s2+2a1
b2(hund) = 5a4+a3+2a2
b3(thou) = 5a4+4a3
b4(tenK) = 6a4
Now include adjustment to ensure each equation, except tenK, is negative:
b0(ones) = a0-4(a4+a3+a2+a1)-20
b1 (tens) = 4a4+6s2+2a1-128
b2(hund) = 5a4+a3+2a2-57
b3(thou) = 5a4+4a3-73
b4(tenK) = 6a4+8
The above polynomials are slightly different from those derived by Mansheim and result in code that runs a little faster. Since this set is for only 17 bits, the maximum value for a_4 was 1. John Anhalt