Page 80 - Handout Digital Electronics

Step 2: Produce the Boolean equations

From the truth table, X = 1 in the input combination, AB = 10, so this is written as:

X = AB ; Y = 1, in the input combination, AB = 01, the Boolean equation is: Y = AB , similarly Z is =1
in the input combinations AB =00 and AB =11, the Boolean equation is:

Z = AB + AB . This expression reduces to: Z = A  B

The logic circuit diagram is produced using the above three Boolean expressions.

Figure 17: Full Comparator logic circuit

Only one output is active at a time depending on the input combinations of A and B. The active output
will give a signal of binary one (1) and the inactive ones will give out binary zeros (0).

Example of input combination AB = 00 giving an output of Z = 1.

Figure 18: Full Comparator operation

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