Combining Logic Gates in Circuits

In real computer circuits, individual logic gates are combined to create more complex operations. OCR J277 Section 2.5 requires you to be able to trace through combined logic gate circuits, complete truth tables for multi-gate circuits, and write Boolean expressions from circuit diagrams.

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How Gates Are Combined

A logic circuit (also called a combinational circuit) connects the output of one gate to the input of another. By chaining gates together, we can create circuits that implement complex Boolean expressions.

For example, to implement the expression Q = (A AND B) OR C, we need:

1. An AND gate taking inputs A and B
2. An OR gate taking the output of the AND gate and input C

  A ----+       +
        | AND   |---+
  B ----+       +   |
                    +---+       +
                    |   |  OR   |---- Q
  C ----------------+   +       +

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Tracing Through a Circuit

To determine the output of a combined circuit for given inputs, follow these steps:

1. Label each gate's output with an intermediate variable (e.g., P, R)
2. Start from the inputs and work left to right through the circuit
3. Calculate each gate's output in order
4. The final gate's output is the circuit's output

Worked Example

Consider the circuit: Q = NOT (A OR B)

With A = 1, B = 0:

Step	Operation	Result
1	A OR B	1 OR 0 = 1
2	NOT (result of step 1)	NOT 1 = 0

So Q = 0.

OCR Exam Tip: When tracing through a circuit, work through one gate at a time, writing down intermediate results. Do not try to calculate the whole circuit in your head — this leads to errors.

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Building a Complete Truth Table for a Circuit

To build a truth table for a circuit with multiple inputs, you need columns for:

• All inputs (A, B, C, etc.)
• All intermediate results (outputs of gates that feed into other gates)
• The final output (Q)

Worked Example

Circuit: Q = (A AND B) OR (NOT A)

A	B	A AND B	NOT A	Q = (A AND B) OR (NOT A)
0	0	0	1	0 OR 1 = 1
0	1	0	1	0 OR 1 = 1
1	0	0	0	0 OR 0 = 0
1	1	1	0	1 OR 0 = 1

The intermediate columns (A AND B and NOT A) make it much easier to get the correct final answer.

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Three-Input Circuits

When a circuit has three inputs (A, B, C), the truth table has 2^3 = 8 rows: