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Adder and subtractor

Adder and subtractor. sneha. Half Adder. A combinational circuit that performs the addition of two bits is called a half adder. It has two inputs. It has two outputs. Truth table: X Y | C S ------------- 0 0 | 0 0 0 1 | 0 1 1 0 | 0 1 1 1 | 1 0. Half adder. Y. X.

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Adder and subtractor

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  1. Adder and subtractor sneha

  2. Half Adder • A combinational circuit that performs the addition of two bits is called a half adder. • It has two inputs. • It has two outputs .

  3. Truth table: X Y | C S ------------- 0 0 | 0 0 0 1 | 0 1 1 0 | 0 1 1 1 | 1 0 Half adder Y X S C

  4. Circuit Diagram

  5. Full Adder • A full adder is a combinational circuit that performs the sum of three bits(two significant bits and a previous carry).

  6. FULL ADDER: Truth table: X Y Cin | C S ------------------- 0 0 0 | 0 0 0 0 1 | 0 1 0 1 0 | 0 1 0 1 1 | 1 0 1 0 0 | 0 1 1 0 1 | 1 0 1 1 1 | 1 0 1 1 1 | 1 1 X Y Full adder Cin C S

  7. Truth table: S = Sm(1,2,4,7) C = Sm(3,5,6,7) • Using K-map, simplified SOP form is: • C = XY + XZ + YZ • S = X'Y'Z + X'YZ'+XY'Z'+XYZ Sum Carry X X 0 1 0 1 YZ YZ 00 0 1 00 0 0 4 4 0 0 01 01 1 0 0 1 Z 5 5 1 1 11 11 0 1 1 1 7 7 3 3 10 1 0 10 0 1 6 6 2 2

  8. Simplified using k-map • Using K-map, simplified SOP form is: C = XY + XZ + YZ S = X'Y'Z + X'YZ'+XY'Z'+XYZ

  9. X Y S (XY) C Z Circuit Diagram • Circuit for above formulae: • C = XY + (XY)Z • S = XYZ (XY) .

  10. Half Adder Half Adder Cin Cin Cin + xy Cin The Full Adder

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