Logic Expressions

A logic expression is a combination of Boolean variables and operators (AND, OR, NOT) that produces a TRUE or FALSE output. Logic expressions can be evaluated using truth tables, and can be represented as logic circuit diagrams.

Writing Logic Expressions

Boolean algebra uses standard notation:

Evaluating Logic Expressions

Example 1: Q = (A AND B) OR (NOT C)

With A=1, B=0, C=1: A AND B = 1 AND 0 = 0; NOT C = NOT 1 = 0; Q = 0 OR 0 = 0

With A=1, B=1, C=1: A AND B = 1; NOT C = 0; Q = 1 OR 0 = 1

Example 2: Full truth table for X = (A OR B) AND (NOT A)

Logic Circuits

A logic circuit diagram shows gates connected together with wires. The output of one gate can feed into another gate's input.

Reading a circuit diagram

To evaluate a circuit for given inputs:

• Work from left to right
• Evaluate each gate in sequence
• Label intermediate outputs (P, Q, etc.)
• The final gate's output is the circuit output

Example: 3-input circuit

A ──┐
    AND → P ──┐
B ──┘         OR → X
C ────────────┘

To evaluate: First find P = A AND B, then find X = P OR C.

Example truth table for the above circuit (Q = (A AND B) OR C)

Order of Evaluation (Precedence)

When no brackets are given, the order is: NOT first, then AND, then OR. Brackets override this order (evaluate innermost brackets first).

NOT A AND B OR C  →  ((NOT A) AND B) OR C
A OR B AND C      →  A OR (B AND C)