Binary Carry-In Calculator

Given two binary signed or unsigned integers (A and B) and their sum or difference (sum), returns the carry-in which happened at each bit position during the addition or subtraction. You can use this on any matching subset of bits of A, B, and sum.

Figuring out the carry-ins has uses for sub-word bit-parallel computations, such as determining if a vector byte addition overflowed into the adjacent byte, but the main use is to get the carry-in into the most-significant bit of a sum. Comparing the final carry-in with the final carry-out allows us to determine if a signed overflow occured, and to compute other arithmetic predicates (e.g.: less-than, greater-than-or-equal, etc...)

`default_nettype none

module CarryIn_Binary
    parameter WORD_WIDTH = 0
    input   wire    [WORD_WIDTH-1:0]    A,
    input   wire    [WORD_WIDTH-1:0]    B,
    input   wire    [WORD_WIDTH-1:0]    sum,
    output  reg     [WORD_WIDTH-1:0]    carryin

    initial begin
        carryin = 1'b0;

Re-add the two integers without carries, which is merely XOR, then compare that carry-less sum with the input sum (this is also an XOR). If the sums differ, then a carry-in was present at that bit position during the input sum.

    always @(*) begin
        carryin = A ^ B ^ sum;


back to FPGA Design Elements