From a Truth Table to a Logic Circuit


If you begin with a truth table instead of an expression, you can write the SOP expression from the truth table and then implement the logic circuit. Table 1 specifies a logic function. 
Table 1

The Boolean SOP expression obtained from the truth table by ORing the product terms for which X = 1 is: X = ABC + AB C

The first term in the expression is formed by ANDing the three variables A, B, and C. The second term is formed by ANDing the three variables A, B, and C.

The logic gates required to implement this expression are as follows: three inverters to form the A, B, and C. variables; two 3-input AND gates to form the terms ABC and AB C; and one 2-input OR gate to form the final output function, ABC + AB C. The implementation of this logic function is illustrated in Figure 1.

Figure 1:  Logic circuit for X = ABC + AB C. Open file F05-11 to verify the
operation.
EXAMPLE  01

Design a logic circuit to implement the operation specified in the truth table:

Solution

Notice that X = 1 for only three of the input conditions. Therefore, the logic expression is: 

The logic gates required are three inverters, three 3-input AND gates and one 3-input OR gate. The logic circuit