1.4.3 Boolean Algebra

Question 1

What are the 6 primary types of logic gates?

Answer 1

AND

OR

NOT

XOR

NAND

NOR

Question 2

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

Answer 2

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

Question 3

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

Answer 3

• Disjunction
• V
  • It is True when any one input is True

Question 4

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

Answer 4

• Negation
• ¬
• It flips a value to its opposite

Question 5

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

Answer 5

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

Question 6

Describe De Morgan’s Law

Answer 6

This states the relationship between AND and OR operators

A ∧ B = ¬(¬A ∨ ¬B)

A ∨ B = ¬(¬A ∧ ¬B)

Question 7

Describe the Distribution law

Answer 7

This law is equivalent to factorising or expanding brackets

X ∨ (Y ∧ Z) = (X ∨ Y) ∧ (X ∨ Z)

Question 8

Describe the Association law

Answer 8

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

X ∧ (Y ∧ X) = (X ∧ Y) ∧ X

Question 9

Describe the Commutation law

Answer 9

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

X ∧ Y = Y ∧ X

Question 10

Describe the Double negation law

Answer 10

This law states a double NOT cancels itself out

¬(¬X) = X

Question 11

Describe the Absorption law

Answer 11

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

X ∨ (X ∧ Y) = X

Question 12

Describe a half adder

Answer 12

A group of logic gates used to add numbers

Question 13

What is a half adder used for?

Answer 13

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

Question 14

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

Answer 14

Question 15

Describe a full adder

Answer 15

A system of logic gates used to add 2 numbers together

Question 16

What is a full adder used for?

Answer 16

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

Question 17

How does a full adder differ from a half adder?

Answer 17

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

Question 18

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

Answer 18

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

Question 19

What is the purpose of a D type flip flop?

Answer 19

To store a previous output for a small period of time

Question 20

What is the principle of a D type flip flop?

Answer 20

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

Question 21

Where are D type flip flops used in a computer?

Answer 21

As memory cells to store bits

Question 22

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

Answer 22

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