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