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

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Presentation on theme: "Binary Addition. Binary Addition (1) Binary Addition (2)"— Presentation transcript:

1 Binary Addition

2 Binary Addition (1)

3 Binary Addition (2)

4 Derivation of ∑ Question: What primitive best implements ∑? Inputs: A, B Outputs: xor (∑, A, B) BA∑ 000 101 011 110

5 Derivation of Carry Out Question: What primitive best implements C o ? Inputs: A, B Outputs: and (C o, A, B) BACoCo 000 100 010 111

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

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

8 Truth Table of ∑ of a Full Adder C in BA∑ 0000 0011 0101 0110 1001 1010 1100 1111 Identical to ∑ of a Half Adder C in +B+A=C in +∑ HA =C in XOR ∑ HA

9 Truth Table of C o of a Full Adder C in BACoCo 0000 0010 0100 0111 1000 1011 1101 1111 Identical to ∑ of a Half Adder Use a Half Adder with C in and ∑ HA to generate C o

10 Schematic of a Full Adder

11 A 3 bit parallel adder


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