The following article was printed in August 1981 of the magazine „BYTE".
A lot of public domain libraries are working on BCD routines.
This article demonstrates an easy way for a conversion.


BinarytoBCD Converter Program for the 8080
D M Brockman, 11648 Military Rd S, Seattle WA 98168

Conversion of multipleprecision binary numbers to BCD (binarycoded decimal) for printing or display output is often encountered in assemblylanguage programming.
The algorithm described here makes use of the 8080's DAA (decimaladjust accumulator) instruction to implement the BCD analogy of a binary shiftleft register.
With this algorithm, a binary number is converted to packed BCD (2 digits per byte) by shifting the binary number, MSB (most significant bit) first, bit by bit, into the least significant end of the BCD register.
(See figure 1.)
When the last binary bit has been shifted in, the result is in the BCD register.

Figure 1:Contents of the BCD and binary registers during the conversion process using the program shown in listing 1.

To understand how the BCD register operates, consider a conventional binaryshift register.
When shifted left, the numeric content doubles and the carry input (if any) comes in at the least significant end.
The same thing happens when the BCD register is "shifted."
The numeric doubling is accomplished by adding the BCD register to itself using BCD arithmetic.
The carry is brought in by using the ADC
(add with carry) instruction for the first "add."
A typical implementation of the algorithm is shown in listing 1 in the form of an 8080 assemblylanguage listing.
Looping constructs have been employed to minimize size.
For maximum speed, the loops should be "unrolled."
The implementation converts a 32bit (4byte) binary number into a 10digit (5byte) packed BCD result.
The number of bytes converted can be easily changed by altering the looping counters.
Note that the number of BCD result bytes required is given by:
Number of BCD bytes = INT(0.5 + 1.204 X (Number of binary bytes))
An advantage of this algorithm is that the conversion time is independent of the size of the number being converted.
The sample routine in listing 1 requires 13,944 machine cycles to execute.
The results of a typical run of the sample routine are shown in table 1.
Memory Address  Before Run  After Run 

BIN:  

0200  3A  00 
0201  F6  00 
0202  23  00 
0203  81  00 

BCD:  

0204  XX  58 
0205  XX  76 
0206  XX  61 
0207  XX  66 
0208  XX  21 
Table 1:A sample run of the binarytoBCD converter program shown in listing 1.
All numbers shown are hexadecimal.
XX indicates a don't care.


Listing 1:
A binarytoBCD Converter program for the Intel 8080 microprocessor.
;TITLE "BINARY TO BCD CONVERTER"
;BY D. M. BROCKMAN, 11648 MILITARY RD. SO., SEATTLE, WA 98168
;
;THIS SUBROUTINE CONVERTS THE 32BIT BINARY NUMBER STORED
; AT 'BIN' TO A 10DIGIT PACKED BCD NUMBER STORED AT 'BCD.'
; REGISTERS B, C, H, L, AND A ARE USED.
;
;
;DEFINE STORAGE FOR NUMBERS:
;
0200 ORG 200H
0200 BIN: DS 1 ;LSB BYTE
0201 DS 2
0203 DS 1 ;MSB BYTE
;
0204 BCD: DS 1 ;LS DIGITS
0205 DS 3
0208 DS 1 ;MS DIGITS
;
;
;INITIALIZE THE BCD RESULT BYTES TO ZERO:
;
0100 ORG 100H
0100 210402 BINBCD: LXI H,BCD ;POINT AT RESULT
0103 0605 MVI B,5 ;SET LOOP COUNTER
0105 3600 ILOOP: MVI M,0 ;STORE A ZERO
0107 23 INX H ;POINT TO SEXT BYTE
0108 05 DCR B ;DECREMENT LOOP COUNTER
0109 C20501 JNZ ILOOP ;LOOP IF NOT DONE
;
;INITIALIZE THE BIT COUNTER TO EQUAL THE NUMBER OF
; BINARY BITS TO BE SHIFTED:
;
010C 0620 MVI B,32 ;NUMBER OF BITS TO SHIFT
CLOOP: ;THE MAIN LOOP POINT
;
;INITIALIZE FOR A MULTIPLE PRECISION LEFT SHIFT
; OF THE BINARY NUMBER:
;
010E 210002 LXI H,BIN ;POINT AT NUMBER
0111 0E04 MVI C,4 ;NUMBER OF BYTES
0113 AF XRA A ;CLEAR THE CARRY
;
;SHIFT THE BINARY NUMBER ONE PLACE LEFT AND LEAVE THE MSB
; IN THE CARRY:
;
0114 7E RLOOP: MOV A,M ;GET BYTE
0115 17 RAL ;SHIFT LEFT
0116 77 MOV M,A ;STORE BYTE
0117 23 INX H ;POINT AT NEXT BYTE
0118 0D DCR C ;DECREMENT BYTE COUNT
0119 C21401 JNZ RLOOP ;LOOP IF NOT DONE
;
;INITIALIZE TO DOUBLE THE BCD RESULT REGISTER CONTENTS
; BY PERFORMING A MULTIPLE PRECISION BCD ADD:
;
011C 210402 LXI H,BCD ;POINT AT RESULT
011F 0E05 MVI C,5 ;SETUP BYTE COUNTER
;
;DOUBLE THE RESULT BCD FASHION, ADDING IN THE CARRY BIT:
;
0121 7E BLOOP: MOV A,M ;GET BYTE
0122 8E ADC M ;ADD IT TO ITSELF
0123 27 DAA ;BCD CONVERT
0124 77 MOV M,A ;RESTORE
0125 23 INX H ;POINT AT NEXT BYTE
0126 0D DCR C ;DECREMENT BYTE COUNTER
0127 C22101 JNZ BLOOP ;LOOP IF NOT DONE
;
;TEST TO SEE IF ALL BITS HAVE BEEN SHIFTED FROM BINARY
; NUMBER TO THE BCD RESULT. IF NOT, RETURN TO MAIN LOOP.
;
012A 05 DCR B ;DECREMENT BIT COUNTER
012B C20E01 JNZ CLOOP ;LOOP IF NOT DONE
012E C9 RET
012F END
A>
[Here as Z80 source]
Scanned by
Werner Cirsovius
September 2002
© BYTE Publications Inc.