AND, OR and NOT

Combining Boolean operators using AND, OR and NOT

2.4.1 Boolean Logic

Boolean Logic — Note 3 of 4

Ability to work with more than one gate in a logic diagram

What you need to know

Logic gates can be combined to form more complex logic circuits and expressions. When combining gates, the order of precedence matters: brackets are evaluated first, then NOT, then AND, then OR. You need to be able to trace through circuits with multiple gates, building the truth table step by step.

What to know

Multiple logic gates can be combined to create complex circuits.
Order of precedence: Brackets > NOT > AND > OR.
Example: B OR NOT C AND A is evaluated as B OR ((NOT C) AND A).
When tracing a combined circuit, work through each gate's output step by step.
Add intermediate columns to truth tables for the output of each gate.
You should be able to write the Boolean expression from a logic circuit diagram.
You should be able to draw a logic circuit from a Boolean expression.

Key terms

Logic Circuit: A combination of interconnected logic gates designed to produce a specific Boolean output.

Exam technique

Tip:When drawing a circuit for a 3-input expression like A AND NOT B AND C, you need a NOT gate for B and TWO AND gates (since AND gates have only 2 inputs). Chain them: e.g. (A AND NOT B) then that result AND C.

Example:P = NOT A AND (B OR C) → draw NOT gate on A, OR gate on B and C, then AND gate combining both outputs.
Example:P = (A OR B) AND NOT C → draw OR gate on A and B, NOT gate on C, then AND gate combining both outputs.

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