### Lecture 6: Logic Circuits (1): Building Boolean Expressions

(Following tutorial's examples are taken from book "Computer Fundamentals - Third Edition". Author: Pradeep K Sinha and Preeti Sinha. Publisher: BPB Publications, New Delhi. Latest version of this book is available for purchase at: www.bpbonline.com)

29.06.12

The logic gates, described in this section, are seldom used alone, but are used in combinations. They interconnected to form gating/logic networks, which are known as combinational logic circuits. For these logic circuits, the Boolean Algebra expression can be derived by systematically progressing from input to output on the gates. Few examples are given below:

Example 1: (In book: Example 6.6, Page: 77)

Find the Boolean expression for the output of the logic circuit given below: This gate is constructed using: 'Logisim'. Download this FOSS from: ozark.hendrix.edu
Solution:
Input A is fed to the NOT gate, whose ouput will be A .
Inputs B and C are fed to the OD gate, whose output will be B + C.
Now two outputs ( A and  B + C) are fed as input to the AND gate. The output produced by AND gate will be A.(B+C).
Hence, D = A.(B+C), which is required Boolean expression for the output of the given logic circuit.

Example 2: (In book: Example 6.7, Page 78)

Find the Boolean expression for the output of the logic circuit given below: This gate is constructed using: 'Logisim'. Download this FOSS from: ozark.hendrix.edu
Solution:
The output of the OR gate is: A + B --------------- (a)
The output of the first AND gate is: A . B -------------- (b)
Since, expression (b) is fed as input to the NOT gate, the output of the NOT gate is: A.B ------------- (c)
Now, expressions (a) and (c) are fed as input to the second AND gate, whose output will be: (A + B) . (A.B)
Hence C = (A + B) . (A.B), which is the desired logic expression for the output produced by the given logic circuit.