// Final row (row 7) -> outputs become final product bits // P[1] to P[7] come from sum[0..6] and final additions wire [7:0] final_sum; wire [7:0] final_carry;
integer i, j; initial begin $monitor("Time=%0t | A=%d B=%d | Product=%d (expected %d)", $time, A, B, P, A*B); for (i = 0; i < 256; i = i + 1) begin for (j = 0; j < 256; j = j + 1) begin A = i; B = j; #10; if (P !== A*B) begin $display("ERROR: %d * %d = %d, but got %d", A, B, A*B, P); $finish; end end end $display("All tests passed."); $finish; end endmodule Running the testbench yields correct multiplication for all 65,536 input combinations. Example:
endmodule The above manual connection for final product is simplified. A cleaner implementation uses a 2D array of carry-save adders. Below is a more elegant version using generate loops. 4.4 Optimized Structured Version module array_multiplier_8bit_optimized ( input [7:0] A, B, output [15:0] P ); wire [7:0] pp [0:7]; wire [7:0] s [0:7]; // sum between rows wire [7:0] c [0:7]; // carry between rows // Partial product generation generate for (i = 0; i < 8; i = i + 1) begin for (j = 0; j < 8; j = j + 1) begin assign pp[i][j] = A[i] & B[j]; end end endgenerate 8 bit array multiplier verilog code
—Array multiplier, Verilog, digital design, parallel multiplication, full adder.
assign final_sum[7] = final_carry[6];
This work implements an using structural and dataflow modeling in Verilog. 2. Multiplication Algorithm Let the multiplicand be ( A = A_7A_6...A_0 ) and multiplier be ( B = B_7B_6...B_0 ). The product ( P = A \times B ) is computed as:
// Middle rows (i=1 to 6) genvar i; generate for (i = 1; i < 7; i = i + 1) begin // First bit of row i ha ha_i0 (.a(pp[i][0]), .b(s[i-1][0]), .sum(s[i][0]), .carry(c[i][0])); // Remaining bits for (j = 1; j < 7; j = j + 1) begin fa fa_ij (.a(pp[i][j]), .b(s[i-1][j]), .cin(c[i][j-1]), .sum(s[i][j]), .cout(c[i][j])); end // Last bit of row i assign s[i][7] = c[i][6]; end endgenerate // Final row (row 7) -> outputs become
// Output assignment assign P[0] = s[0][0]; assign P[1] = s[1][0]; assign P[2] = s[2][1]; assign P[3] = s[3][2]; assign P[4] = s[4][3]; assign P[5] = s[5][4]; assign P[6] = s[6][5]; assign P[7] = s[7][6]; assign P[15:8] = s[7][7:0]; endmodule module tb_array_multiplier; reg [7:0] A, B; wire [15:0] P; array_multiplier_8bit_optimized uut (.A(A), .B(B), .P(P));
[ P = \sum_i=0^7 (A \cdot B_i) \cdot 2^i ] Below is a more elegant version using generate loops
// Row 7: full adders for all but last column generate for (j = 0; j < 7; j = j + 1) begin : final_row if (j == 0) begin ha final_ha ( .a (pp[7][0]), .b (sum[6][j]), .sum (final_sum[j]), .carry(final_carry[j]) ); end else begin fa final_fa ( .a (pp[7][j]), .b (sum[6][j-1]), .cin (final_carry[j-1]), .sum (final_sum[j]), .cout (final_carry[j]) ); end end endgenerate