Binary-to-BCD Converter Program for the 8080

D M Brockman, 11648 Military Rd S, Seattle WA 98168

Conversion of multiple-precision binary numbers to BCD (binary-coded decimal) for printing or display output is often encountered in assembly-language programming. The algorithm described here makes use of the 8080's DAA (decimal-adjust accumulator) instruction to implement the BCD analogy of a binary shift-left 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 binary-shift 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 assembly-language listing. Looping constructs have been employed to minimize size. For maximum speed, the loops should be "unrolled." The implementation converts a 32-bit (4-byte) binary number into a 10-digit (5-byte) 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 binary-to-BCD converter program shown in listing 1. All numbers shown are hexadecimal. XX indicates a don't care.

Listing 1:

A binary-to-BCD 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 32-BIT BINARY NUMBER STORED ; AT 'BIN' TO A 10-DIGIT 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]