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Logic Gates and Boolean Algebra

Boolean notation and expressions

  • 3 things to know
  • AS Unit 1

Overview

Recall questions on how AND, OR, NOT and XOR are written, why AND is written like multiplication and where the addition analogy breaks down, operator precedence, evaluating expressions, writing one for an alarm circuit, and why brackets matter.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Evaluation

How is XOR written in Boolean notation, why is AND written as multiplication, and how are two mixed expressions evaluated?

Key term

How is the OR operation written in Boolean algebra?

Key term

What symbol is conventionally used for XOR?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How is the AND operation written in Boolean algebra?

    Model answer

    It is written as a dot between the variables, as in A·B, or by writing them next to each other as AB, following the convention of multiplication.

  2. 2

    How is the OR operation written in Boolean algebra?

    Model answer

    It is written with a plus sign between the variables, as in A + B, following the convention of addition.

  3. 3

    How is the NOT operation written?

    Model answer

    It is written as a bar drawn over the variable, or in plain text as ¬A, and it means the complement of that value.

  4. 4

    What symbol is conventionally used for XOR?

    Model answer

    XOR is written with a plus sign inside a circle, as in A ⊕ B.

  5. 5

    Why is AND written like multiplication?

    Model answer

    Because 0·0, 0·1 and 1·0 all give 0 while 1·1 gives 1, which is exactly what ordinary multiplication of 0 and 1 does.

  6. 6

    Where does the analogy between OR and ordinary addition break down?

    Model answer

    It breaks down at 1 + 1, which in Boolean algebra is 1 rather than 2, because a Boolean value can only ever be 0 or 1.

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