// half adder component used in the multiplier
module half_adder(a, b, s, cout);

input  a, b;
output s, cout;

assign s = a^b; 
assign cout = a&b;

endmodule

// full adder component used in the multiplier
module full_adder(a, b, cin, s, cout);

input  a, b, cin;
output s, cout;

assign s = a^b^cin; 
assign cout = (a&b) | (b&cin) | (a&cin);

endmodule

// 3-bit by 3-bit unsigned multiplier
module mult3(x, y, p);

input  [2:0] x, y;
output [5:0] p;

// internal nodes within the multiplier circuit
wire   t1, t2, t3, t4, t5, t6, t7;

// structural description of the multiplier circuit
assign p[0] = x[0]&y[0];
half_adder ha1(x[1]&y[0], x[0]&y[1], p[1], t1);
half_adder ha2(x[2]&y[0], x[1]&y[1], t2, t3);
full_adder fa1(t2, t1, x[0]&y[2], p[2], t4);
full_adder fa2(x[2]&y[1], t3, x[1]&y[2], t5, t6);
half_adder ha3(t5, t4, p[3], t7);
full_adder fa3(x[2]&y[2], t6, t7, p[4], p[5]);

endmodule