1.4.3 Boolean Algebra Flashcards Preview

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Flashcards in 1.4.3 Boolean Algebra Deck (22)
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1

What are the 6 primary types of logic gates?

AND

OR

NOT

XOR

NAND

NOR

2

What is the name, gate diagram, symbol, and explanation for an AND gate?

  • Conjunction
  • Ʌ

  • Only produces a True output if both inputs are True

3

What is the name, gate diagram, symbol, and explanation for an OR gate?

  • Disjunction
  • V

    • It is True when any one input is True

4

What is the name, gate diagram, symbol, and explanation for a NOT gate?

  • Negation
  • ¬

  • It flips a value to its opposite

5

What is the name, gate diagram, symbol, and explanation for an XOR gate?

  • Exclusive Disjunction
  • V

  • True when any one input is True, but not when both are True

6

Describe De Morgan's Law

This states the relationship between AND and OR operators

A ∧ B = ¬(¬A ∨ ¬B)

A ∨ B = ¬(¬A ∧ ¬B)

7

Describe the Distribution law

This law is equivalent to factorising or expanding brackets

X ∨ (Y ∧ Z) = (X ∨ Y) ∧ (X ∨ Z)

8

Describe the Association law

This law states that when using multiple operations of the same type, the operand order doesn't matter

X ∧ (Y ∧ X) = (X ∧ Y) ∧ X

9

Describe the Commutation law

This law states it doesn't matter which side of an AND or OR gate the operands are on

X ∧ Y = Y ∧ X

10

Describe the Double negation law

This law states a double NOT cancels itself out

¬(¬X) = X

11

Describe the Absorption law

This law states that something ORed/ANDed with the AND/OR of itself and another is equal to the original

X ∨ (X ∧ Y) = X

12

Describe a half adder

A group of logic gates used to add numbers

13

What is a half adder used for?

Taking 2 single-bit numbers and adding them together, producing a digit bit and a carry bit

14

What does the logic circuit of a half adder look like?

15

Describe a full adder

A system of logic gates used to add 2 numbers together

16

What is a full adder used for?

Adding 2 one-bit binary numbers with an incoming carry bit, producing a digit bit and a carry bit

17

How does a full adder differ from a half adder?

It can take 3 single-bit numbers rather than just 2

18

What does the logic circuit of a full adder look like?

Two half adders with an OR gate between the carry(out)-bits

19

What is the purpose of a D type flip flop?

To store a previous output for a small period of time

20

What is the principle of a D type flip flop?

Changes the values of the output when the clock input is momentarily increased (up tick)

21

Where are D type flip flops used in a computer?

As memory cells to store bits

22

How does the bit stored in a D type flip flop change?

An upward tick of a clock pulse will cause the output to take the value of whatever is being input