Boolean Expressions from Logic Diagrams
When a logic circuit is given, the Boolean expression describing that logic circuit can be obtained by combining the input variables in accordance with the logic gate functions. The procedure is best illustrated with the examples that follow.
For the logic circuit shown below find D = f(A, B, C), that is, express the output D in terms of the inputs A, B , and C. If possible, simplify the Boolean expression obtained, and implement it with a simplified logic diagram.
Example 1:
Solution:
We label the output of each gate as shown in below diagram
Outputs of the gates of logic diagram
The simplified logic diagram is shown in Figure below
Example 2:
To derive the Boolean expression for a given combinational logic circuit, begin at the left-most inputs and work toward the final output, writing the expression for each gate.
Determine the Boolean expression for the following logic circuit
Solution: A.(B+ CD)
Example 3:
Solution: AB + A(B + C) + B(B + C)
Circuit Diagrams from Boolean Expressions
Now we will try to draw a circuit diagram from the given boolean expression
Example 1:
Q = B(A + C)
