Let x = y * z (multiplication)

multiplies two 16-bit values into a 16-bit product, permitting overflow.

PBASIC allows you to multiply any two variables together--bits, bytes, words, or a mixture--to get a 16-bit product. If the product is larger than 16 bits, the highest-order bits are lost.

This isn't as much of a handicap as it might sound. Users of the BASIC Stamp have managed to get excellent results by carefully designing their programs to avoid overflow. The benefit of working within this limitation is that the routine required to do this sort of math is compact and reasonably fast.

Multiplication of binary numbers works just like the long-form multiplication you learned in school, only it's much easier. Instead of multiplication tables, all you need is this general rule: n x 0 = 0; and n x 1 = n. Arrange the numbers in the traditional way, and you're ready to go:

Although the product of two 16-bit numbers is a 32-bit number, note that in this case the first 16 bits of the product are all 0s and can be safely ignored.

Demonstrating Multiply.

To see Multiply in operation, either run the program with the PSIM simulator, or connect the circuit below to an erasable PIC or PIC emulator, such as the Parallax downloader. Assemble and run MULTIPLY.SRC. When you apply power to the PIC, the LEDs will light up in the binary pattern of the answer to the math problem 0Bh * 1016h, which is B0F2h. The product displays the following binary pattern on the LEDs:

1011 0000 1111 0010

Try multiplying various values to see different results.
 

;
; ***************************************************************************
; ***  Bubble Software Parallax to PIC Source Converter. Copyright 1999.  ***
; ***  http://www.bubblesoftonline.com                 email: sales@picnpoke.com  ***
; ***************************************************************************
;
; MULTIPLY multiplier, multiplicand
; Multiply two 16-bit numbers into a 16-bit product, permitting overflow. 

; Device data and reset vector
	P = pic16c55
	#include <16c55.inc>   ; processor assembler definitions
	_CONFIG _xt_osc & _wdt_off & _protect_off
        reset   start

        org     8
mulcH   Res      d'1'       ; MSB of multiplicand. 
mulcL   Res      d'1'       ; LSB of multiplicand. 
mulpH   Res      d'1'       ; MSB of multiplier.
mulpL   Res      d'1'       ; LSB of multiplier.
prodH   Res      d'1'       ; MSB of product. 
prodL   Res      d'1'       ; LSB of product. 
index   Res      d'1'       ; temporary counter

        org     0

start        MOVLW d'0'                 ; Outputs for LEDs to 
             TRIS 6h
             MOVLW d'0'                 ; display 16-bit result.
             TRIS 7h
             MOVLW d'0'                 ; Problem: multiply
             MOVWF mulcH
             MOVLW 0x0B                 ; 0Bh by 1016h
             MOVWF mulcL
             MOVLW 0x10                 
             MOVWF mulpH
             MOVLW 0x16                 
             MOVWF mulpL
             CALL multiply              
             MOVF prodL,w               ; Show result in binary on 
             MOVWF 6h
             MOVF prodH,w               ; LEDs connected to ports.
             MOVWF 7h
             GOTO $                     ; Endless loop

Multiply
             CLRF prodH                 ; Clear product to make
             CLRF prodL                 ; way for new calculation.
             MOVLW d'16'                ; Number of bits to calc. 
             MOVWF index
Multiply_loop
             BCF status,c               
             RLF prodL                  ; Shift product left.
             RLF prodH                  
             BCF status,c               
             RLF mulcL                  ; Shift multiplicand left.
             RLF mulcH                  
             BTFSS status,c             ; If carry, add multiplier
             GOTO Multiply_skip
             MOVF mulpL,w               ; to the product. Else skip.
             ADDWF prodL
             BTFSC status,c             ; 16-bit addition: prod+mulp
             INCF prodH                 
             MOVF mulpH,w               
             ADDWF prodH
Multiply_skip
             DECFSZ index               
             GOTO Multiply_loop
             RETLW 0h                   
             
             
             end

; MULTIPLY multiplier, multiplicand
; Multiply two 16-bit numbers into a 16-bit product, permitting overflow. 
        org     8
mulcH   ds      1       ; MSB of multiplicand. 
mulcL   ds      1       ; LSB of multiplicand. 
mulpH   ds      1       ; MSB of multiplier.
mulpL   ds      1       ; LSB of multiplier.
prodH   ds      1       ; MSB of product. 
prodL   ds      1       ; LSB of product. 
index   ds      1       ; temporary counter

; Device data and reset vector
        device  pic16c55,xt_osc,wdt_off,protect_off
        reset   start
        org     0

start	mov	!rb,#0		; Outputs for LEDs to 
	mov	!rc,#0		; display 16-bit result.
	mov	mulcH,#0	; Problem: multiply
	mov	mulcL,#0Bh	; 0Bh by 1016h
	mov	mulpH,#10h
	mov	mulpL,#16h
	call	multiply
	mov	rb,prodL	; Show result in binary on 
	mov	rc,prodH	; LEDs connected to ports.
	jmp	$		; Endless loop

Multiply
	clr	prodH		; Clear product to make
	clr	prodL		; way for new calculation.
	mov	index,#16	; Number of bits to calc. 
:loop	clc
	rl	prodL		; Shift product left.
	rl	prodH
	clc
	rl	mulcL		; Shift multiplicand left.
	rl	mulcH
	jnc	:skip		; If carry, add multiplier
	ADD	prodL,mulpL	; to the product. Else skip.
	snc			; 16-bit addition: prod+mulp
	inc	prodH
	ADD	prodH,mulpH
:skip	djnz	index,:loop
	ret

See also:

• http://www.piclist.com/techref/microchip/math/basic.htm

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