Binary Addition. Binary Addition (1) Binary Addition (2)

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Presentation transcript:

Binary Addition

Binary Addition (1)

Binary Addition (2)

Derivation of ∑ Question: What primitive best implements ∑? Inputs: A, B Outputs: xor (∑, A, B) BA∑

Derivation of Carry Out Question: What primitive best implements C o ? Inputs: A, B Outputs: and (C o, A, B) BACoCo

A Half Adder A half adder is useful for adding LSB.

Limitation of a Half Adder A half-adder does not account for carry-in.

Truth Table of ∑ of a Full Adder C in BA∑ Identical to ∑ of a Half Adder C in +B+A=C in +∑ HA =C in XOR ∑ HA

Truth Table of C o of a Full Adder C in BACoCo Identical to ∑ of a Half Adder Use a Half Adder with C in and ∑ HA to generate C o

Schematic of a Full Adder

A 3 bit parallel adder