Hii Brent Kung adder is a parallel prefix adder. Parallel prefix adder are high performance carry tree adder in which pre-computing of propagation and generation signal take place.Due to the complexity (log2n) delay through the carry path, the parallel-prefix tree adders are more favourable in terms of speed as compared to other adders. It consumed less area and has maximum depth. The number of cell of Brent Kung adder can be calculated by (2n-1) –log2n and the delay of the structure is (2log2 n-2). The three steps are generally used for design a Brent Kung adder: Step-1: It involves the creation of generate and propagate signals for the input operand bits. Step-2: This involves the generation of carry signals Step-3: In this step the sum bits of the adder following stages of the operand bits and the preceding stage carry bit using a XOR gate The below figure shows the schematic of 16 bit brent kung adder. module badd16( input [15:0] a, input [15:0] b, output [16:0] sum ); wire [15:0] p; wire [15:0] g; wire [15:0] cp1; wire [15:0] cg1; wire cp22; wire cg22; wire cp23; wire cg23; wire cp27; wire cg27; wire cp34; wire cg34; wire cp35; wire cg35; wire cp36; wire cg36; wire cp37; wire cg37; wire cp211; wire cg211; wire cp215; wire cg215; wire cp315; wire cg315; wire cp411; wire cg411; wire cp415; wire cg415; wire cp59; wire cg59; wire cp513; wire cg513; wire cp68; wire cg68; wire cp610; wire cg610; wire cp612; wire cg612; wire cp614; wire cg614; wire [16:0] s; // start fist level assign p[0] = a[0] ^ b[0];//first level zero bit start assign g[0] = a[0] & b[0]; assign cp1[0] = p[0]; assign cg1[0] = g[0]; //first level zero bit complete assign p[1] = a[1] ^ b[1]; //first level first bit start assign g[1] = a[1] & b[1]; assign cg1[1] = (p[1] & g[0])| g[1]; assign cp1[1] = p[1] & p[0]; // first level first bit complete assign p[2] = a[2] ^ b[2]; //first level 2nd bit start assign g[2] = a[2] & b[2]; assign cp1[2] = p[2]; assign cg1[2] = g[2]; // first level 2nd bit complete assign p[3] = a[3] ^ b[3]; //first level 3rd bit start assign g[3] = a[3] & b[3]; assign cg1[3] = (p[3] & g[2]) | g[3]; assign cp1[3] = p[3] & p[2]; //first level 3rd bit complete assign p[4] = a[4] ^ b[4]; //first level 3rd bit start assign g[4] = a[4] & b[4]; assign cg1[4] = g[4]; assign cp1[4] = p[4]; //first level 3rd bit complete assign p[5] = a[5] ^ b[5]; //first level 3rd bit start assign g[5] = a[5] & b[5]; assign cg1[5] = (p[5] & g[4]) | g[5]; assign cp1[5] = p[5] & p[4]; //first level 3rd bit complete assign p[6] = a[6] ^ b[6]; //first level 3rd bit start assign g[6] = a[6] & b[6]; assign cg1[6] = g[6]; assign cp1[6] = p[6]; //first level 3rd bit complete assign p[7] = a[7] ^ b[7]; assign g[7] = a[7] & b[7]; assign cg1[7] = (p[7] & g[6]) | g[7]; assign cp1[7] = p[7] & p[6]; assign p[8] = a[8] ^ b[8]; assign g[8] = a[8] & b[8]; assign cg1[8] = g[8]; assign cp1[8] = p[8]; assign p[9] = a[9] ^ b[9]; assign g[9] = a[9] & b[9]; assign cg1[9] = (p[9] & g[8]) | g[9]; assign cp1[9] = p[9] & p[8]; assign p[10] = a[10] ^ b[10]; assign g[10] = a[10] & b[10]; assign cg1[10] = g[10]; assign cp1[10] = p[10]; assign p[11] = a[11] ^ b[11]; assign g[11] = a[11] & b[11]; assign cg1[11] = g[11]; assign cp1[11] = p[11]; assign p[12] = a[12] ^ b[12]; assign g[12] = a[12] & b[12]; assign cg1[12] = g[12]; assign cp1[12] = p[12]; assign p[13] = a[13] ^ b[13]; assign g[13] = a[13] & b[13]; assign cg1[13] = (p[13] & g[12]) | g[13]; assign cp1[13] = p[13] & p[12]; assign p[14] = a[14] ^ b[14]; assign g[14] = a[14] & b[14]; assign cg1[14] = g[14]; assign cp1[14] = p[14]; assign p[15] = a[15] ^ b[15]; assign g[15] = a[15] & b[15]; assign cg1[15] = (p[15] & g[14]) | g[15]; assign cp1[15] = p[15] & p[14]; assign cp22 = cp1[2] & cp1[1]; assign cg22 = (cp1[2] & cg1[1]) | cg1[2]; assign cg23 = (cp1[3] & cg1[1]) | cg1[3]; assign cp23 = cp1[3] & cp1[1]; assign cg27 = (cp1[7] & cg1[5]) | cg1[7]; assign cp27 = cp1[7] & cp1[5]; assign cg34 = (cp1[4] & cg23) | cg1[4]; assign cp34 = cp1[4] & cp23; assign cg35 = (cp1[5] & cg23) | cg1[5]; assign cp35 = cp1[5] & cp23; assign cg36 = (cp1[6] & cg35) | cg1[6]; assign cp36 = cp1[6] & cp35; assign cg37 = (cp27 & cg23) | cg27; assign cp37 = cp27 & cp23; assign cg211 = (cp1[11] & cg1[9]) | cg1[11]; assign cp211 = cp1[11] & cp1[9]; assign cg215 = (cp1[15] & cg1[11]) | cg1[15]; assign cp215 = cp1[15] & cp1[11]; assign cg315 = (cp215 & cg211) | cg215; assign cp315 = cp215 & cp211; assign cg411 = (cp211 & cg37) | cg211; assign cp411 = cp211 & cp37; assign cg415 = (cp315 & cg37) | cg315; assign cp415 = cp315 & cp37; assign cg59 = (cp1[9] & cg37) | cg1[9]; assign cp59 = cp1[9] & cp37; assign cg513 = (cp1[13] & cg411) | cg1[13]; assign cp513 = cp1[13] & cp411; assign cg68 = (cp1[8] & cg37) | cg1[8]; assign cp68 = cp1[8] & cp37; assign cg610 = (cp1[10] & cg59) | cg1[10]; assign cp610 = cp1[10] & cp59; assign cg612 = (cp1[12] & cg411) | cg1[12]; assign cp612 = cp1[12] & cp411; assign cg614 = (cp1[14] & cg513) | cg1[14]; assign cp614 = cp1[14] & cp513; assign s[0] = p[0]; assign s[1] = p[1] ^ cg1[0]; assign s[2] = p[2] ^ cg1[1]; assign s[3] = p[3] ^ cg22; assign s[4] = p[4] ^ cg23; assign s[5] = p[5] ^ cg34; assign s[6] = p[6] ^ cg35; assign s[7] = p[7] ^ cg36; assign s[8] = p[8] ^ cg37; assign s[9] = p[9] ^ cg68; assign s[10] = p[10] ^ cg59; assign s[11] = p[11] ^ cg610; assign s[12] = p[12] ^ cg411; assign s[13] = p[13] ^ cg612; assign s[14] = p[14] ^ cg513; assign s[15] = p[15] ^ cg614; assign s[16] = cg415; assign sum = {s[16:0]}; endmodule
I spotted a couple of bugs in this Verilog adder. The first occurs in the assignment of cg1[11] and cp1[[1], which I patched as follows: Code: if (FIX) begin assign cg1[11] = (p[11] & g[10]) | g[11]; assign cp1[11] = p[11] & p[10]; end else begin // original code assign cg1[11] = g[11]; assign cp1[11] = p[11]; end (where FIX is an added localparam set to 1). Without this fix you get a bad sum when you add a=16'h0001 to b=16'0BFF, for example. The sum should be 17'h00C00, but the original code produced 17'h01C00. The second bug is in the assignment of cg215 and cp215, which I patched as follows. Here, the propagate/generate expressions should span two bits to bit #13, and not four bits to bit #11 as the original code specified. Code: if (FIX) begin assign cg215 = (cp1[15] & cg1[13]) | cg1[15]; assign cp215 = cp1[15] & cp1[13]; end else begin // original code assign cg215 = (cp1[15] & cg1[11]) | cg1[15]; assign cp215 = cp1[15] & cp1[11]; end Without this fix, when you add a=16'h0001 to b=16'hCFFF, the sum 17'h1D000 is produced, where the correct sum should be 17'h0D000. I ran the patched 16-bit adder on a Nexys 4 board running at 100MHz, in a bitfile comparing the adder results against several other 16-bit adders. It runs fine now with those two patches. I attach my patched file, which includes a few comments related to a few wires which appeared to run at somewhat confusing levels. But this is just a naming issue, nothing more.