1. ADDERS
Half Adders
Recall that the basic rules of binary addition are as indicated below in Table 2-9. A circuit known as the half-adder carries out these basic operations. The half-adder, illustrated in next slide, accepts two binary digits and produces the sum and carry digits.

2. Adders
Half Adder
A+B
Sum
Carry
0+0
0+1 1
1+0
1+1

3. Half ADDER

4. Half ADDER
Observe from Table 2-9 that we may derive logical expressions for the Sum (S) and carry output (CO) bits. Namely,     CO = AB, and . From these two expressions, the implementation of the half-adder function is developed as illustrated in next slide

5. Logic Circuit for half-adder

6. Full Adder
The second basic category of adder is the full-adder. This combinational circuit performs the arithmetic addition of three input bits. The noticeable difference between the full- and the half-adder is the ability of the former to handle input carries (CI). The logical symbol for the half-adder is shown in earlier slides and the associated truth table in earlier table.

7. Truth Table for FA A B
Cin  Co 1

8. FULL ADDER

9. FULL ADDER
By the very nature of the full adder we know that the two input bits must be added to the carry input bit. Recall that for the half-adder the sum of A and B is the XOR of those two variables,. Similarly, for the three variables A, B and CI the sum becomes . This is illustrated in next slide

10. FULL ADDER
SUM Values

11. FULL ADDER

12. Two Half ADDER