Binary Addition Section 4.5. Binary Addition Example.

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Presentation transcript:

Binary Addition Section 4.5

Binary Addition Example

Binary Addition (2)

Derivation of ∑ BA∑

Derivation of Carry Out Question: What primitive best implements C o ? Inputs: A, B Outputs: C o =A∙B BACoCo

Implementation of a Half-Adder

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

Truth Table for a Full Adder carry-in

Karnaugh Map For the Sum Bit

Karnaugh Map For the Carry-Out Bit

Implementation of a Full Adder (carry-in)

Four-Bit Adder C 4 is calculated last because it takes C 0 8 gates to reach C 4.

Alternative Naming Convention for the Full Adder

Hardware Simplification 2 gate delays for C 3 !

Four-bit adder with Carry Lookahead