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69. Binary Subtractor

A. Dataflow

module sub4_2c (
    input  [3:0] a,
    input  [3:0] b,
    output [3:0] diff,
    output       bout
);
    // Width-safe 5-bit add to capture carry-out
    wire [4:0] sum5 = {1'b0, a} + {1'b0, ~b} + 5'b00001;
    assign diff = sum5[3:0];
    assign bout = ~sum5[4]; // borrow = NOT carry-out
endmodule

B. Structural via ripple adder

module full_adder_1bit(
    input  a, b, cin,
    output sum, cout
);
    assign sum  = a ^ b ^ cin;
    assign cout = (a & b) | (b & cin) | (a & cin);
endmodule

module rca4_add (
    input  [3:0] x, y,
    input        cin,
    output [3:0] sum,
    output       cout
);
    wire c1, c2, c3;
    full_adder_1bit fa0(.a(x[0]), .b(y[0]), .cin(cin), .sum(sum[0]), .cout(c1));
    full_adder_1bit fa1(.a(x[1]), .b(y[1]), .cin(c1 ), .sum(sum[1]), .cout(c2));
    full_adder_1bit fa2(.a(x[2]), .b(y[2]), .cin(c2 ), .sum(sum[2]), .cout(c3));
    full_adder_1bit fa3(.a(x[3]), .b(y[3]), .cin(c3 ), .sum(sum[3]), .cout(cout));
endmodule

module sub4_2c (
    input  [3:0] a,
    input  [3:0] b,
    output [3:0] diff,
    output       bout
);
    wire [3:0] b_inv = ~b;
    wire       cout;
    rca4_add adder(.x(a), .y(b_inv), .cin(1'b1), .sum(diff), .cout(cout));
    assign bout = ~cout;
endmodule

💡Remember

  • Two’s complement subtraction = invert b, add 1, then add to a.
  • For unsigned subtraction, borrow-out = NOT carry-out from the addition.
  • For signed 4-bit subtraction, the carry is irrelevant; overflow is detected with sign bits (not required here).
  • Keep everything combinational (use assign or always @* with proper defaults).