Logic circuit diagrams
Logic Circuit Diagrams
A logic circuit diagram is a visual representation showing how logic gates are connected together to produce an output. Each gate is drawn using its standard symbol, and wires (lines) carry signals between gates. Circuit diagrams allow us to see at a glance which conditions must be true for the output to be 1, and are used extensively in the design of CPUs and digital electronics.
Three skills are required: interpreting an existing circuit (tracing inputs through gates to find the output), creating a new circuit from a description or expression, and modifying an existing circuit by changing a gate and understanding how the output behaviour changes as a result.
Gate Symbol Reference
Each gate has a specific standard symbol. These symbols must be drawn and recognised correctly - rectangles or labelled boxes are not acceptable substitutes in exam answers.
Left to right: NOT (yellow), AND (blue), OR (green), XOR (orange). Input wires enter from the left; the output wire exits from the right.
Interpreting, Creating and Modifying Circuits
Interpreting a Circuit: (NOT A) AND B
To interpret a circuit, trace each input through every gate from left to right. Evaluate any NOT gates first (they affect the signal before it reaches the next gate), then evaluate the final gate using the values that arrive at its inputs.
To trace this circuit: the signal from A passes through the NOT gate and is inverted before reaching the AND gate. Input B goes directly to the AND gate. The AND gate outputs 1 only when both its inputs are 1 - meaning NOT A = 1 (so A must be 0) and B = 1.
| A | B | NOT A | Q = (NOT A) AND B |
|---|---|---|---|
| 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
Interpretation: Q is 1 in only one case: when A = 0 and B = 1. Whenever A = 1, the NOT gate blocks the AND gate regardless of B. This circuit detects "B is active but A is not".
Creating a Circuit: A OR (NOT B)
To build a circuit from the expression A OR (NOT B), work from the innermost brackets outward, then connect gates in order:
- The expression has two parts feeding into OR: input A, and the result of NOT B.
- Draw a NOT gate. Connect input B to its input. The NOT output will become the lower input to the OR gate.
- Draw an OR gate to the right. Connect input A directly to its upper input. Connect the NOT gate output to its lower input.
- The OR gate output is Q.
Key rule when creating circuits: draw gates in the order that signals flow - from input towards output. Any gate whose output feeds into another gate must be drawn first (to its left). Input wires that go directly to a gate without passing through another gate can travel any horizontal distance.
Modifying a Circuit: AND Changed to OR
Consider the circuit (NOT A) AND B from the first tab. Suppose we modify it by replacing the AND gate with an OR gate, giving (NOT A) OR B. The wire connections remain identical - only the gate symbol changes. The output behaviour, however, changes significantly.
The circuit now implements (NOT A) OR B. Comparing truth tables shows how the change affects every row:
| A | B | NOT A | (NOT A) AND B | (NOT A) OR B |
|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 |
Swapping AND for OR changes Q from being active in only 1 row to being active in 3 rows. The only case where Q remains 0 is when A = 1 and B = 0, because then NOT A = 0 and B = 0, so OR gives 0. Modifying a single gate can therefore dramatically alter what a circuit does.
Key Takeaways
- Each logic gate has a specific standard symbol: NOT = triangle with output circle; AND = D-shape; OR = curved with pointed output; XOR = OR with extra curved line on the input side.
- To interpret a circuit, trace each input left to right through every gate, evaluating intermediate values before the final output.
- To create a circuit, identify which gates are needed from the Boolean expression, draw inner operations first (closest to inputs), and connect outputs to the next gate's inputs.
- To modify a circuit, change the gate symbol and redraw - the wire connections may remain the same, but the truth table and output behaviour will change.
- A NOT gate placed before another gate inverts its input signal, which can block or enable the next gate depending on the input value.