Section 4.2
Evaluating Logic Circuit Outputs

Once the Boolean expression for a circuit output has been obtained, the output logic level can be determined for any set of input levels.

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This are two examples of the evaluating logic circuit output:

Let A=0, B=1, C=1, D=1

X	= A'BC (A+D)'
	= 0'*1*1* (0+1)'
	= 1 *1*1* (1)'
	= 1 *1*1* 0
	= 0

 

Let A=0, B=0, C=1, D=1, E=1

X	= [D+ ((A+B)C)'] * E
	= [1 + ((0+0)1 )'] * 1
	= [1 + (0*1)'] * 1
	= [1+ 0'] *1
	= [1+ 1 ] * 1
	= 1

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In general, the following rules must always be followed when evaluating a Boolean expression:

1. First, perform all inversions of single terms; that is, 0 = 1 or 1 = 0.
2. Then perform all operations within parentheses.
3. Perform an AND operation before an OR operation unless parentheses indicate otherwise.
4. If an expression has a bar over it, perform the operations of the expression first and then invert the result.

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Determining Output Level from a Diagram

The output logic level for given input levels can also be determined directly from the circuit diagram without using the Boolean expression.