Adders:
Adders are the Digital Logic Circuits which adds binary digits.
There are two type of Adders
a) Half Adder
b) Full Adder
a) Half Adder
b) Full Adder
Half Adder:
It is a logic circuit that add 2 binary bits.
Truth Table for Half Adder
A | B | Carry | Sum |
0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 |
1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 |
Boolean Expression:
Sum: A'B + AB'
Carry: A.B
*** The expressions are derived by taking values of A & B, where value of Sum & Carry are "1".
also, in S.O.P expression assertion is "1" & negation is "0".
Logic Circuit Diagram:
Full Adder:
It is a logic circuit that add 3 binary bits.
Truth Table for Full Adder
A | B | C | Carry | Sum |
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 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 |
Boolean Expression:
Sum: A'B'C + A'BC' + AB'C' + ABC
Carry: A'BC + AB'C + ABC' + ABC
= A'BC + AB'C + AB(C' +C) (Distributive Law)
= A'BC + AB'C + AB(1) (Complementarity Law)
= A'BC + AB'C + AB (Property of 1)
= A'BC + A(B'C + B)
= A'BC + A(B'+B)(B+C) (Distributive Law)
= A'BC + A(1)(B+C) (Complementarity Law)
= A'BC + A(B+C) (Property of 1)
= A'BC + AB + AC (Distributive Law)
= B(A'C + A) + AC
= B(A'+A)(C + A) + AC (Distributive Law)
= B(1)(C + A) + AC (Complementarity Law)
= B(C + A) + AC (Property of 1)
= BC + AB + AC (Distributive Law)
= AB + BC + AC (Commutative Law
Logic Circuit Diagram:
Full Adder Using Two Half Adders:
Truth Table : Same as Full Adder.
Boolean Expression : Same as Full Adder.
Logic Circuit Diagram:
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