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" ;)

 

[DeeNos]

for your question. It is possible to use 4x4 bit multipliers to perform an 8x8 bit multiplication, but it would require some additional steps compared to using an 8x8 bit multiplier.

First, let's define what a multiplier is. A multiplier is a digital circuit that performs the operation of multiplication on two binary numbers. In this case, we are dealing with 8-bit binary numbers, which means each number has 8 bits (or 8 binary digits).

A 4x4 bit multiplier is a digital circuit that can multiply two 4-bit binary numbers. To use this 4x4 bit multiplier to perform an 8x8 bit multiplication, we would need to break down the 8-bit numbers into two 4-bit numbers each.

For example, if we have two 8-bit numbers, A = 11001101 and B = 10101010, we can break them down into four 4-bit numbers as follows:

A = 1100 1101
B = 1010 1010

Now, we can use the 4x4 bit multiplier to multiply each pair of 4-bit numbers, resulting in four 8-bit partial products. These partial products can then be added together to get the final product.

In this case, the four partial products would be:

P1 = 1100 x 1010 = 11110000
P2 = 1100 x 1010 = 11110000
P3 = 1101 x 1010 = 11100110
P4 = 1101 x 1010 = 11100110

Adding these partial products together, we get the final product:
11110000 + 11110000 + 11100110 + 11100110 = 100111010000

This is an 8x8 bit multiplication using 4x4 bit multipliers. As you can see, it requires more steps and calculations compared to using an 8x8 bit multiplier, which can directly multiply two 8-bit numbers. However, in some cases, using smaller multipliers can be more efficient in terms of circuit complexity and speed.

I hope this helps to answer your question. Let me know if you have any further inquiries.