Question 13.13: Simplifyinga Logic Circuit by Using the Karnaugh Map Derive ...
Simplifyinga Logic Circuit by Using the Karnaugh Map
Derive the Karnaugh map corresponding to the circuit of Figure 13.43 and use the resulting map to simplify the expression.
Known Quantities: Logic circuit.
Find: Simplified logic circuit.
Analysis: We first determine the expression f(x, y, z) from the logic circuit:
f=(x \cdot z)+(\bar{x} \cdot \bar{z})+(y \cdot \bar{z})
This expression leads to the Karnaugh map shown in Figure 13.44. Inspection of the Karnaugh map reveals that the map could have been covered more efficiently by using four-cell subcubes. The improved map covering, corresponding to the simpler function f=x+\bar{z}, and the resulting logic circuit are shown in Figure 13.45.
Comments: In general, one wishes to cover the largest possible subcubes in a Karnaugh map.
