CODEWITHSUNDEEP
algorithm
Rednil
Rednil

Reputation: 13

Binary multiplication with addition

I have an exercise where I am supposed to multiply an unknown number by 5. The number is max 8 bits and stored in 2's compliment. So if the number is 5 the result should be 25 and if its -12 it should be -60.

My only tools are load a register with a bit pattern and add two bit patterns together and store the result. I'm only allowed to use addition 3 times in my program.

With a known number I think I could solve it by adding the appropriate bit pattern to make it 5 times bigger but will that work with an unknown number?

Ex. I have the bit pattern 0001010 representing 10 knowing I want 50 as the result I would add the bit pattern 0101000 to get the resulting 0110010 which is 50.

Can someone please give me a hint how I can solve this problem thank you!

Upvotes: 1

Views: 288

Answers (1)

Paul Hankin
Paul Hankin

Reputation: 58359

You can compute 5x=2x+2x+x using three additions. Something like this:

y = x + x  // y = 2x
z = y + y  // z = 2y = 4x
r = z + x  // r = 4x + x = 5x

If x is the unknown value, then at the end of this code, r is x * 5.

Upvotes: 4

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