logic-gatesmultiplier
I have an assignment that requires building 4-bit Multiplier in two ways:
1) using only FA1bit and AND logic gates.
2) using only FA8bit(Full adder for 8bit numbers) , Mul2bit(Multiplier for numbers with 2 bits) and AND logic gates .
i figured out the first way , but i cant figure out how to do the second way .
(of course im talking about binary numbers)
thanks
My notation: n x n → m
Two operands with length "n" bits and product with length "m" bits.
1. Multiplication result depends on operands being signed /unsigned
Ex. 4x4 → 8:
Fh x Fh = E1h, unsigned integer: 15 x 15
Fh x Fh = 01h, signed integer: -1 x -1
Note: The 4 LSbs are the same for signed and unsigned multiplication.
2. Signed product Fh x 8h (-1 x -8) depends on target size
4 x 4 → 8: 08h (or 8), OK
4 x 4 → 4: 8h (or -8), INCORRECT (overflow).
Generalization: Negating (or getting the two's complement) a byte containing -128, a word containing -32768, or a double word containing -2147483648, cause no changing in the operand, but the NEG instruction will set the overflow flag (ex. for x86 architecture).
If you combine two half adders you get the carry-in functionality. Here's a half adder: -
And here's a full adder: -
Can you see what has happened i.e. two half adders are combined to make a full adder: -
So, in effect you have made an 8 bit adder using both "building blocks".
Best Answer
You need to think about how you multiply decimal numbers by hand.
Now, think of your two 4-bit binary numbers as being written in base 4.
Do you see the analogy? Do you see how 2-bit multipliers might apply?