How to multiply a number by 42 in 8086 assembly without using MUL or DIV and in 5 lines?-CodePudding

I have this problem where I am asked to multiply BX by 42 without using any mul or div instructions, presumably by using shl or shr. It is also required to do it in 5 lines.

How do you do such a thing ?

I didn't try anything, but the above requirement was to multiply BX by 32 in 1 line, so I just used SHL BX, 5.

CodePudding user response：

Factor 42 (decimal) equals 00101010 (binary), and orders of 1s in this notation are 1, 3, 5, hence the result will be
2¹ * N 2³ * N 2⁵ * N = 42 * N.

The code assumes CPU Intel 186 or better and the factor N loaded in BX; product is returned in BX, too.
Unfortunately, it needs six instructions, I didn't manage to spare a line.

SHL BX,1   ; BX=2*N
MOV AX,BX  ; AX=2*N
SHL BX,2   ; BX=8*N
ADD AX,BX  ; AX=2*N   8*N
SHL BX,2   ; BX=32*N
ADD BX,AX  ; BX=2*N   8*N   32*N = 42*N

CodePudding user response：

A trio of solutions that have 6 lines and can run on emu8086 because that emulator does allow shifting by an immediate count, contrary to what a real 8086 CPU would allow!

On input BX = N

shl bx, 1   ; BX = N * 2 
mov ax, bx  ; AX = N * 2
shl bx, 2   ; BX = N * 8
add bx, ax  ; BX = N * 10
shl bx, 2   ; BX = N * 40
add bx, ax  ; BX = N * 42

mov ax, bx  ; AX = N
shl bx, 2   ; BX = N * 4
add ax, bx  ; AX = N * 5
shl bx, 2   ; BX = N * 16
add bx, ax  ; BX = N * 21
shl bx, 1   ; BX = N * 42

but the above requirement was to multiply BX by 32 in 1 line

mov ax, bx  ; AX = N
shl bx, 5   ; BX = N * 32
shl ax, 1   ; AX = N * 2 
add bx, ax  ; BX = N * 34
shl ax, 2   ; AX = N * 8
add bx, ax  ; BX = N * 42