Boolean algebra

Question 1

what is a logic gate?

Answer 1

an electronic circuit designed to perform logical operations on one or more binary inputs to produce a single output

Question 2

what is a truth table?

Answer 2

a table that lists all possible combinations of inputs and their corresponding outputs

Question 3

how is a NOT gate represented?

Answer 3

symbol: triangle pointing in direction of flow with a circle next to it, 1 input, 1 output
mathematical: ¬A
engineering: A̅

Question 4

draw the truth table for a NOT gate (negation)

Answer 4

A | Q
1 | 0
0 | 1

Question 5

how is an AND gate represented?

Answer 5

symbol: looks like a D with 2 inputs, 1 output
mathematical: A ∧ B
engineering: A.B

Question 6

draw the truth table for an AND gate (conjunction)

Answer 6

A | B | Q
0 | 0 | 0
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1

Question 7

how is an OR gate represented?

Answer 7

symbol: like a curved arrowhead - pointy end up front, curved end behind, 2 inputs, 1 output
mathematical: A ∨ B
engineering: A + B

Question 8

draw the truth table for an OR gate (disjunction)

Answer 8

A | B | Q
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 1

Question 9

how is an XOR gate represented?

Answer 9

symbol: like an OR gate but with an extra line behind it too
mathematical: A ⊻ B
engineering: A ⊕ B

Question 10

draw the truth table for an XOR gate (exclusive disjunction)

Answer 10

A | B | Q
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0

Question 11

what strategies can be used to simplify a boolean expression?

Answer 11

• collecting like terms
• factorising
• following the laws to simplify expressions within the expression

Question 12

what are the general rules of boolean algebra?
(all here in engineering coz its easier)

Answer 12

A.0 = 0
A.1 = A
A.A = A
A.A̅ = 0
A + 0 = A
A + 1 = 1
A + A = A
A + A̅ = 1

Question 13

what is the commutative law of boolean algebra?
(in engineering notation)

Answer 13

A + B = B + A
A.B = B.A

Question 14

what is the associate law of boolean algebra?

Answer 14

A + (B + C) = (A + B) + C
A.(B.C) = (A.B).C

Question 15

what is the distributive law of boolean algebra?

Answer 15

A.(B + C) = A.B + A.C
A + (B.C) = (A+B).(A+C)

Question 16

what is the absorption/redundancy law of boolean algebra?

Answer 16

A + A.B = A
A.(A + B) = A

Question 17

what are de Morgan’s laws of boolean algebra?

Answer 17

(A̅+̅B̅) = A̅.B̅
(A̅.̅B̅) = A̅ + B̅
(basically break the bar, change the sign)