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The Language of Logic
The Language of Logic
Boolean expressions are how we write logic in text form, like algebra for true/false values. Instead of drawing circuit diagrams, we can write "A AND B" or "NOT(A OR B)". Named after George Boole, who invented this mathematical logic in the 1800s - long before computers! His maths became the foundation of all digital computing. Every IF statement you write is a Boolean expression.
Deep Dive: George Boole and the Birth of Binary Logic
George Boole (1815-1864) was an English mathematician who revolutionized logic by treating it as algebra. He asked: "What if we could do maths with TRUE and FALSE instead of numbers?" His answer became Boolean algebra - a system where variables can only be 1 (true) or 0 (false).
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Exam Tips - Boolean Expressions
When writing Boolean expressions:
- Use brackets liberally - makes order of operations crystal clear
- Be consistent - don't mix "AND" with "∧" in same answer
- GCSE boards accept: AND/OR/NOT or symbols ∧/∨/¬ - choose what you're comfortable with
- Check your NOT placement: NOT(A AND B) is very different from NOT(A) AND B
When evaluating expressions:
- Show ALL steps - write out intermediate values for method marks
- Work inside-out: Brackets first, then NOT, then AND, finally OR
- Substitute values clearly: Write "NOT(1) = 0" not just "0"
- Double-check: Re-evaluate your final answer with original values
Common mistakes to avoid:
- NOT(A AND B) ≠ NOT(A) AND NOT(B) - these are DIFFERENT!
- Forgetting brackets when needed - A AND B OR C is ambiguous
- Missing the difference between NOT(A) AND B vs NOT(A AND B)
- Writing A·B without defining that · means AND in your answer
Translation tips (English to Boolean):
- "Both" / "all" → AND operation
- "Either" / "or" / "at least one" → OR operation
- "Not" / "opposite" / "false" → NOT operation
- "Only when A but not B" → A AND NOT(B)
Now try it yourself
Quiz · Question 1 of 17
Which Boolean operator produces an output of 1 only when BOTH inputs are 1?
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This topic in real past papers
Every real exam question we've found on boolean expressions, with a full worked answer.