Generating Schematic Diagrams from Boolean Expressions The two truth tables should be identical. If you would like to verify this, you may generate a truth table for both expressions and determine Q’s status (the circuits’ output) for all eight logic-state combinations of A, B, and C, for both circuits. The final expression, B(A + C), is much simpler than the original, yet performs the same function. Now that we have a Boolean expression to work with, we need to apply the rules of Boolean algebra to reduce the expression to its simplest form (simplest defined as requiring the fewest gates to implement): then another sub-expression for the next gate:įinally, the output (“Q”) is seen to be equal to the expression AB + BC(B + C): Remember that OR gates are equivalent to Boolean addition, while AND gates are equivalent to Boolean multiplication.įor example, I’ll write sub-expressions at the outputs of the first three gates: This task is easily performed step by step if we start by writing sub-expressions at the output of each gate, corresponding to the respective input signals for each gate. Our first step in simplification must be to write a Boolean expression for this circuit. How to Write a Boolean Expression to Simplify Circuits Where these signals originate is of no concern in the task of gate reduction. The “A,” “B,” and “C” input signals are assumed to be provided from switches, sensors, or perhaps other gate circuits. Let’s begin with a semiconductor gate circuit in need of simplification.

Sequential circuits examples