Using 4x4 bit multipiers to do an 8x8 bit multiply

[murraymuz]

Hi
How would I use 4x4bit multipliers to calculate an 8x8 bit multiply?

Thanks

 

[0xDEADBEEF]

Sounds like homework. Imagine how you do multiplication of large numbers on paper and you might understand how to rebuild it with a few adders and multipliers.

 

[murraymuz]

This is'nt really homework because I have'nt been set it, I'm trying to teach myself this in advance.

I want to perform the calculation 232 x 111 using 4bit multipliers?

First show them in their binary form.
1 1 1 0 1 0 0 0 =232
0 1 1 0 1 1 1 1 =111

Second split the binary number so that one 4x4 multiply does the higher bits and one the lower bits.

Multiply 1 (left bits)
1 1 1 0 14
0 1 1 0 6
Multiply 2 (right bits)
1 0 0 0 8
1 1 1 1 15
Multiply 1 – 8 bit answer
0 1 0 1 0 1 0 0
Multiply 2– 8 bit answer
0 1 1 1 1 0 0 0

Third step is to combine the two answers together by placing them next to each other.
Final binary answer
32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1
0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 = 21624

The technique I have used here seems right but I get the wrong answer, does anyone know where I have gone wrong?
thanks

 

[0xDEADBEEF]

So if you multiply two numbers by hand let's say 53 and 24 you do this?

5*2 = 10 (two digits)
3*4 = 12

and then you write them next to each other? 53*24=1012 ?

No this is false what you do is this

53*24

5(0)*2(0) = 10(00)
5(0)*4 = 20(0)
3*2(0) = 6(0)
3*4 = 12

and then you do 1000+200+60+12 = 1272

Now maybe you can see how to translate this into binary. It's http://www.youtube.com/watch?v=DfCJgC2zezw" ;)