1.4.3 Boolean Algebra Flashcards Preview

A Level Computer Science > 1.4.3 Boolean Algebra > Flashcards

Flashcards in 1.4.3 Boolean Algebra Deck (22)
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1
Q

What are the 6 primary types of logic gates?

A

AND

OR

NOT

XOR

NAND

NOR

2
Q

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

A
  • Conjunction
  • Ʌ
  • Only produces a True output if both inputs are True
3
Q

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

A
  • Disjunction
  • V
    • It is True when any one input is True
4
Q

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

A
  • Negation
  • ¬
  • It flips a value to its opposite
5
Q

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

A
  • Exclusive Disjunction
  • V
  • True when any one input is True, but not when both are True
6
Q

Describe De Morgan’s Law

A

This states the relationship between AND and OR operators

A ∧ B = ¬(¬A ∨ ¬B)

A ∨ B = ¬(¬A ∧ ¬B)

7
Q

Describe the Distribution law

A

This law is equivalent to factorising or expanding brackets

X ∨ (Y ∧ Z) = (X ∨ Y) ∧ (X ∨ Z)

8
Q

Describe the Association law

A

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
Q

Describe the Commutation law

A

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

X ∧ Y = Y ∧ X

10
Q

Describe the Double negation law

A

This law states a double NOT cancels itself out

¬(¬X) = X

11
Q

Describe the Absorption law

A

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
Q

Describe a half adder

A

A group of logic gates used to add numbers

13
Q

What is a half adder used for?

A

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

14
Q

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

A
15
Q

Describe a full adder

A

A system of logic gates used to add 2 numbers together

16
Q

What is a full adder used for?

A

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

17
Q

How does a full adder differ from a half adder?

A

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

18
Q

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

A

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

19
Q

What is the purpose of a D type flip flop?

A

To store a previous output for a small period of time

20
Q

What is the principle of a D type flip flop?

A

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

21
Q

Where are D type flip flops used in a computer?

A

As memory cells to store bits

22
Q

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

A

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