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Half Adder

A half adder is the simplest arithmetic circuit that adds two single-bit numbers.

Truth Table​

ABSumCarry
0000
0110
1010
1101

Logic​

  • Sum = A XOR B (outputs 1 when inputs differ)
  • Carry = A AND B (outputs 1 when both inputs are 1)

SHDL Implementation​

component HalfAdder(A, B) -> (Sum, Carry) {
    xor1: XOR;
    and1: AND;
    
    connect {
        A -> xor1.A;
        B -> xor1.B;
        A -> and1.A;
        B -> and1.B;
        xor1.O -> Sum;
        and1.O -> Carry;
    }
}

Circuit Diagram​

    A ───┬──────► XOR ────► Sum
         │          ▲
         │          │
    B ───┼──────────┘
         │
         └──────► AND ────► Carry
         ▲
         │
    B ───┘

Usage​

The half adder is the building block for:

  • Full adders (by adding a carry input)
  • Multi-bit adders
  • ALUs