You are asked to design a 2-bit unsigned binary multiplier. The multiplier takes

ID: 3833943 • Letter: Y

Question

You are asked to design a 2-bit unsigned binary multiplier.

The multiplier takes two 2-bit inputs, A[1:0] and B[1:0], and produces an output Y[n-1:0]

which is the product of these two numbers:

Y[n-1:0] = A[1:0] * B[1:0]

a. (1 point) What is the maximum value that can be represented by one of the inputs?

b. (1 point) What is the maximum value that Y will ever have?

c. (1 point) What is the value of n, the number of output bits?

d. (8 points) Construct the complete truth table for the multiplier: you will have four inputs: (A[1], A[0], B[1]

and B[0]), and n outputs

e.Extract from the table the boolean expression for bit 1 of the output (considering, as always bit

as the lsb), simplify it to the extent possible, and draw the corresponding logic circuit.

a) Both the inputs are of two bit so maximum value is 11 in binary and 3 in decimal.

b) When both the inputs have maximun value only then output is maximum so maximum output value is 1001 in binary and 9 in decimal.

c) Value of n is 4 . The maximum output is 1001 so it use 4 bits.

d) Truth table :

*****INPUT1**************** *********INPUT2************ ********************OUTPUT******************************

A[1]

A[0]

B[1]

B[0]

Y[3]

Y[2]

Y[1]

Y[0]