16-bit BCD

The following code for ca65 converts a 16-bit unsigned integer to decimal digits, in roughly 700 cycles, without using the decimal mode that was removed from the 2A03.

To understand how curDigit is used, see Wikipedia:Ring counter.

<source lang="6502">

bcd16.s

version 20060201

Copyright (C) 2006 Damian Yerrick

Copying and distribution of this file, with or without

modification, are permitted in any medium without royalty provided

the copyright notice and this notice are preserved in any source

code copies. This file is offered as-is, without any warranty.

.p02

.exportzp bcdNum, bcdResult .export bcdConvert

bcdConvert

Given a number in bcdNum (16-bit), converts it to 5 decimal digits

in bcdResult. Unlike most 6502 binary-to-decimal converters, this

subroutine doesn't use the decimal mode that was removed from the

2A03 variant of the 6502 processor.

For each value of n from 4 to 1, it compares the number to 8*10^n,

then 4*10^n, then 2*10^n, then 1*10^n, each time subtracting if

possible. After finishing all the comparisons and subtractions in

each decimal place value, it writes the digit to the output array

as a byte value in the range [0, 9]. Finally, it writes the

remainder to element 0.

Extension to 24-bit and larger numbers is straightforward

Add a third bcdTable, increase BCD_BITS, and extend the

trial subtraction.

Constants _________________________________________________________

BCD_BITS

The highest possible number of bits in the BCD output. Should

roughly equal 4 * log10(2) * x, where x is the width in bits

of the largest binary number to be put in bcdNum.

bcdTableLo[y], bcdTableHi[y]

Contains (1 << y) converted from BCD to binary.

BCD_BITS = 19

Variables _________________________________________________________

bcdNum (input)

Number to be converted to decimal (16-bit little endian).

Overwritten.

bcdResult (output)

Decimal digits of result (5-digit little endian).

X

Offset of current digit being worked on.

Y

Offset into bcdTable*.

curDigit

The lower holds the digit being constructed.

The upper nibble contains a sentinel value; when a 1 is shifted

out, the byte is complete and should be copied to result.

(This behavior is called a "ring counter".)

Overwritten.

b

Low byte of the result of trial subtraction.

Overwritten.

bcdNum = 0 bcdResult = 2 curDigit = 7 b = 2

Completes within 670 cycles.

bcdConvert:

 lda #$80 >> ((BCD_BITS - 1) & 3)
 sta curDigit
 ldx #(BCD_BITS - 1) >> 2
 ldy #BCD_BITS - 5

@loop:

 ; Trial subtract this bit to A:b
 sec
 lda bcdNum
 sbc bcdTableLo,y
 sta b
 lda bcdNum+1
 sbc bcdTableHi,y

 ; If A:b > bcdNum then bcdNum = A:b
 bcc @trial_lower
 sta bcdNum+1
 lda b
 sta bcdNum

@trial_lower:

 ; Copy bit from carry into digit and pick up 
 ; end-of-digit sentinel into carry
 rol curDigit
 dey
 bcc @loop

 ; Copy digit into result
 lda curDigit
 sta bcdResult,x
 lda #$10  ; Empty digit; sentinel at 4 bits
 sta curDigit
 ; If there are digits left, do those
 dex
 bne @loop
 lda bcdNum
 sta bcdResult
 rts

bcdTableLo:

 .byt <10, <20, <40, <80
 .byt <100, <200, <400, <800
 .byt <1000, <2000, <4000, <8000
 .byt <10000, <20000, <40000

bcdTableHi:

 .byt >10, >20, >40, >80
 .byt >100, >200, >400, >800
 .byt >1000, >2000, >4000, >8000
 .byt >10000, >20000, >40000

</source>

See also

• HexToDecimal.8