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Unformatted text preview: s usually used to represent a NOR operation in Boolean expressions.
Thus, A ↓ B = A + B = A .B
Inputs Output A B C = A-B 0
0 Figure 6.26. Block diagram symbol and the truth table for a NOR gate.
The operation of a NOR gate can be analyzed using the equivalent block diagram circuit
shown in Figure 6.27, which has an OR gate followed by a NOT gate. For inputs A and
B, the output of the OR gate will be A + B, which is fed as input to the NOT gate. Hence
the complement of A + B will be A + B, which is equal to A • B
or A * B . In fact, the small circle on the output of the NOR gate (see Figure 6.26)
represents complementation. The NOR gate can then be seen to be an OR gate followed
by a NOT gate.
Multiple input NOR gates can be analyzed similarly. A three-input NOR gate with inputs
A, B, and C will have an output equal to A + B + C or A-B-C, which says that the output
will be a 1 only when all the three inputs are 0 and it will be a 0 if any of the three inputs
is a 1.
The logic gates described in the previous section are seldom used by themselves but are
used in combinations. They are 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.
Find the Boolean expression for the output of the logic circuit given below.
Input A is fed to the.NOT gate whose output will be A.
Inputs B and C are fed to the OR gate whose output will be B + C.
Now these two outputs (A and B + C) are fed as input to the AND gate. The output
produced by the AND gate will be A • (B + C).
Hence, D = A • (B + C), which is the required Boolean expression for the output of the
given logic circuit. Example 6.7.
Find the logic equation for the output produced by the logic circuit given below.
The output of the OR gate is
A + B -------------- (a)
The output of the first AND gate is
A • B --------------- (b)
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This document was uploaded on 04/07/2014.
- Spring '14