Logic Circuits

A logic circuit is a physical implementation of a Boolean expression using interconnected logic gates. In OCR H446, you need to be able to draw circuits from Boolean expressions, trace circuits to produce truth tables, and understand multi-level circuits with several stages of gates.

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From Boolean Expression to Circuit

To convert a Boolean expression into a circuit:

1. Identify the main operation (the last operation to be evaluated) — this determines the output gate
2. Work backwards through the expression, adding gates for each sub-expression
3. Connect inputs to the appropriate gates
4. Label all wires clearly

Example: Draw the circuit for Q = (A AND B) OR (NOT C)

The main operation is OR, so the output gate is OR.

• Input 1 to the OR gate: A AND B (requires an AND gate with inputs A and B)
• Input 2 to the OR gate: NOT C (requires a NOT gate with input C)

Circuit structure:

A ---+
     |--- AND ---+
B ---+           |--- OR --- Q
                 |
C --- NOT -------+

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From Circuit to Boolean Expression

To determine the expression from a circuit: