Half Adder

XOR for sum, AND for carry — the simplest adder circuit.

Interactive Circuit
A
B
Sum
0
Carry
0
Circuit Diagram
A=0B=0XORANDSum=0Carry=0
Boolean Equations
SumA ⊕ B = 00= 0
CarryA ∧ B = 00= 0
0 + 0 = 00 (0 in decimal)
Truth Table
ABSumCarry
0000
0110
1010
1101
About the Half Adder
The half adder adds two single bits and produces a sum and a carry. It uses an XOR gate for the sum (1 when inputs differ) and an AND gate for the carry (1 only when both inputs are 1). It's called "half" because it has no carry-in — it can only add the least-significant column of a multi-bit addition.