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Binary Addition
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Binary Addition (1)
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Binary Addition (2)
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Derivation of ∑ Question: What primitive best implements ∑? Inputs: A, B Outputs: xor (∑, A, B) BA∑ 000 101 011 110
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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
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A Half Adder A half adder is useful for adding LSB.
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Limitation of a Half Adder A half-adder does not account for carry-in.
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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
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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
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Schematic of a Full Adder
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A 3 bit parallel adder
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