(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 |

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.
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