Digital Electronics
Explainer
How Logic Gates Add Binary Numbers
Every sum your processor computes starts with one XOR and one AND gate.
Quick check · tap an answer to continue
Lesson notes
Key points
- A half adder adds two bits, giving a Sum output and a Carry output, with no carry input.
- Its Sum is A XOR B, and its Carry is A AND B, since only one plus one produces a carry.
- A full adder also accepts a carry-in, so it can chain bits; it can be built from two half adders and an OR gate.
- Chaining full adders, each carry-out feeding the next carry-in, creates a ripple-carry adder for multi-bit numbers.
Definitions
- Half adder
- Combinational circuit adding two bits A and B to produce Sum and Carry outputs.
Takeaway: Half adder: Sum = A XOR B, Carry = A AND B; full adders chain.
Quick check: What is the Carry output of a half adder?
- A XOR B
- A OR B
- A AND B
Half adderSum and CarryFull adderRipple carry
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