Page 87 - Cs_withBlue_J_C11_Flipbook
P. 87
Example 3: Draw the logic circuit diagram of the Boolean expression ((A'+B+C).(B+C'))'.
Ans. The gate sequence will be (A' OR B OR C) NAND (B OR C') or NOT((A’ OR B OR C) AND (B OR C’) ).
A' (A'+B+C)
B
C
((A'+B+C).(B+C'))'
C' (B+C')
Example 4: Derive the Boolean expression for the following logic circuit.
A
B
C
Ans.
A A'.B+A.B'
B
(C.(A'.B+A.B'))'
C
Hence, the derived expression is (C.(A'.B + A.B'))'.
Example 5: Derive the Boolean expression for the following logic circuit.
A
B
C
Ans.
A A'.B'+A.B
B
(A'.B'+A.B).(B+C)'
C (B+C)'
Hence, the derived expression is (A'.B' + A.B).(B+C)'
3.8 HALF ADDER AND FULL ADDER
In digital systems, combinational circuits are designed to perform various data processing tasks like addition,
subtraction, multiplication, complement, shift, increment, decrement, etc. One such combinational circuit is the adder,
which performs the addition of binary numbers. Adders are of two types: (i) Half Adder and (ii) Full Adder.
85
Propositional Logic, Hardware Implementation, Arithmetic Operations 85

