Page 208 - Introduction to Microcontrollers Architecture, Programming, and Interfacing of The Motorola 68HC12

7.2 Integer Conversion 185

where 0 £ q < b for 0 <. i < m. The sequence c m _[,.. . CQ is called an m-digit base-b
representation of N. We are interested in going from the representation of N in one base
to its representation in another base. There are two common schemes for this conversion
that are based on multiplication and two schemes that are based on division. Although
one of the division schemes is taught in introductory logic design courses, and you are
likely to select it because you know it well, it does not turn out to be the most efficient
to implement in a microcomputer. We look at all the schemes in general and then give
examples of each to find the most promising one.
The two multiplication schemes simply carry out (3), doing the arithmetic in the
base that we want the answer in. There are two ways to do this. Either evaluate
expression (3) as it appears or else nest the terms as shown.
N = ( ... ( 0 + c m_, ) * b + c m_ 2) *b+.. . + c, )*b+c o (4)

The other two schemes involve division. Notice from (3) that if you divide N by b, the
remainder is CQ. Dividing the quotient by b again yields c\, and so forth, until one of the
quotients becomes 0. In particular, if one has a base-r representation of N and wants to
go to a base-b representation, division of N by b is done in base-r arithmetic. You are

*
* SUBROUTINE CVDTB puts the unsigned equivalent of five ASCII decimal digits
* pointed to by X into D.
*
SCRATCH: ds. b 6 ; Scratch area for product and multiplier
Kt dc.w 10000,1000,100,10,1 ; Coefficient Vector
*
CVDTB: LDAB #6 ; Clear scratch area
LDY #SCRATCH
Cl: CLR 1,Y+
DBNE B,C1
*
LDAB #5 ; Five terms to be evaluated
LDY #K ; Constants in vector K, Y = multiplicand address
*
C2: LDAA 1,X+ ; Next ASCII digit into A
PSHX ; Save pointer for next character
SUBA #$30 ; ASCII to binary
STAA SCRATCH*5 ; Save in last byte in scratch
LDX #SCRATCH+4 ; Get address of multiplier
EMACS SCRATCH ; Multiply and accumulate
LEAY 2, Y ; Next multiplicand address
PULX ; Restore pointer for next character
DBNE B, C2 ; Count down and loop
LDD SCRATCH+2 ; Get number
RTS ; Return to Caller
Figure 7.4. Conversion from Decimal to Binary by Multiplication by Powers of 10