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Logic gates and Boolean logic

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Lesson notes

Boolean logic

  • Boolean logic works with values True (1) and False (0). Computer circuits are built from logic gates that process binary inputs.

The main gates

  • NOT (inverter): output is the opposite of the input. NOT 0 = 1; NOT 1 = 0.
  • AND: output is 1 only if both inputs are 1.
  • OR: output is 1 if at least one input is 1.
  • (Some courses also use XOR: output 1 if the inputs are different; and NAND, NOR.)

AND requires both inputs

AND requires both inputsABANDQABQ000010100111

Truth tables

  • A truth table lists all input combinations and the output. For two inputs there are 4 rows (00, 01, 10, 11).
  • AND: 0 0 0 1 (for 00, 01, 10, 11). OR: 0 1 1 1. XOR: 0 1 1 0.

All four input combinations

All four input combinationsABORQABQ000011101111

Combining gates

  • Gates can be combined into logic diagrams. Q = (A AND B) OR C. For three inputs there are 8 rows.
  • Write a Boolean expression (A AND B, NOT A) and work out each output step by step.

Q = (A AND B) OR C

Q = (A AND B) OR CABCANDORQABCQ00000011010001111000101111011111

Uses

  • Logic gates are the basis of processors, memory, alarms and decision circuits, e.g. a car alarm sounding if (door open AND ignition off).

Slides

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Practice questions

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  1. 1.What is Boolean logic?

    Easy
    • Alogic using True and False values
    • Blogic using text
    • Clogic using colour
    • Dlogic using hardware

  2. 2.What does a NOT gate do?

    Easy
    • Ainverts the input
    • Badds inputs
    • Cchooses the larger
    • Dstores a bit

  3. 3.What is the output of OR with inputs 0 and 0?

    Easy
    • A0
    • B1
    • C10
    • Dundefined

  4. 4.What is the output of OR with inputs 1 and 0?

    Easy
    • A1
    • B0
    • C10
    • Dundefined

  5. 5.What is the output of AND with inputs 1 and 1?

    Easy
    • A1
    • B0
    • C2
    • D11

  6. 6.What is NOT 1?

    Easy
    • A0
    • B1
    • C2
    • Dundefined

  7. 7.What is the output of XOR with inputs 1 and 1?

    Easy
    • A0
    • B1
    • C2
    • Dundefined

  8. 8.What is the output of XOR with inputs 1 and 0?

    Easy
    • A1
    • B0
    • C2
    • Dundefined

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