Question

Design an array multiplier that multiplies two 2-bit unsigned fixed-point operands: multiplicand A = [1:0] and multiplier B = [1:0]. The product is P[3:0]. Obtain the structural design module using only AND gates and half adders. Obtain the test bench for all combinations of the multiplicand and multiplier, the outputs, and waveforms.

Answer 1

To design an array multiplier using only AND gates and half adders, we can use the principle of Boolean algebra to multiply two 2-bit unsigned fixed-point operands. The structural design module of the array multiplier involves creating partial products using AND gates and summing them using half adders. Additionally, the test bench can be created to simulate all combinations of the operands and observe the outputs and waveforms.

Step-by-step explanation:

To design an array multiplier using only AND gates and half adders, we can use the principle of Boolean algebra. Each digit of the multiplicand is multiplied by each digit of the multiplier, and the results are added together to form the final product. Here is the structural design module:

module ArrayMultiplier(A, B, P);
input [1:0] A, B;
output [3:0] P;
wire [3:0] P0, P1;

// Partial products
and #(4) P0_and(A[0], B[0:1], P0);
and #(4) P1_and(A[1], B[0:1], P1);

// Sum of partial products
half_adder HA0(P0[0], P1[0], P[0], P[1]);
half_adder HA1(P0[1], P1[1], P[1], P[2]);
half_adder HA2(P0[2], P1[2], P[2], P[3]);
endmodule

To obtain the test-bench, we need to generate all combinations of the multiplicand and multiplier, provide inputs to the module accordingly, simulate the module, and observe the outputs and waveforms. Here is an example of the test-bench:

module ArrayMultiplier_tb;
reg [1:0] A, B;
wire [3:0] P;

ArrayMultiplier DUT(.A(A), .B(B), .P(P));

initial begin
// Generate all combinations of A and B
repeat(4) begin
A = $random;
B = $random;
#10;
// Print inputs and outputs
$display("A = %b, B = %b, P = %b", A, B, P);
end
$finish;
end
endmodule