Page 213 - Introduction to Microcontrollers Architecture, Programming, and Interfacing of The Motorola 68HC12

190 Chapter? Arithmetic Operations

An improved technique shown in Figure 7.7 uses division, rather than successive
subtraction, to speed up the algorithm, but it has the same difficulties as the one in
Figure 7.3; larger numbers require a larger table of constants. We now look at the other
division scheme. For example, if the contents of D is divided by 10, the remainder is the
binary expansion of NQ. Dividing this quotient by 10 yields a remainder equal to the
binary expansion of Nj, and so on. See Figure 7.8a. This approach can be implemented
by a recursive algorithm. See Figure 7.8b.
Suppose that we wanted to convert a 16-bit unsigned binary integer in D to the
equivalent decimal number using the best multiplication technique, in particular, the one
that used (4) instead of (3). Write the binary expansion of the number bjs , bo in
decimal notation as

and assume that the equivalent five-decimal digits are to be placed at the address passed in
X, with one decimal digit stored per byte in binary. (We can convert each digit to ASCII
later, if necessary.) After initializing the result to 0, we iteratively build the equivalent
decimal number from the innermost parentheses above by repeating the following steps:

* CVBTD converts the 16-bit unsigned number in D to an equivalent 6-digit BCD
* number stored in 3 bytes at the address passed in by the calling routine in X.
*
CVBTD: PSHD ; Save number to be converted
CLR 0,X
CLR 1,X
CLR 2, X ; Initialize decimal number
MOVE #16,1, -SP ; Push count
*
CBD1: ASL 2,SP
ROL 1, SP ; Put next bit in C
LDAB #2 ; 3-byte decimal addition
*
CBD2; LDAA B,X ; Get ith byte
ADCA B, X ; Adding a number to itself doubles it
DAA ; Double in decimal
STAA B, X ; Put back ith byte
*
DECB
BPL CBD2 ; Count down and loop 3 bytes
DEC 0,SP
BNE CBD1 ; Count down and loop 16 bits
*
LEAS 3, SP ; Balance stack
RTS

Figure 7.9. Conversion from Binary to Decimal by Decimal Multiplication