Boolean logic and algebra

Question 1

Boolean logic for AND, OR and NOT

Answer 1

AND = A.B
OR = A+B
NOT = Ā

Question 2

Why would you simplify circuits

Answer 2

Less logic gates means simpler circuits meaning cheaper designs and cheaper processers etc.

Question 3

How can you simplify circuits

Answer 3

Using algebra or truth tables

Question 4

List all 8 Boolean algebraic identifiers

Answer 4

0+A = A

1+A = 1

A+A = A

A+Ā = 1

0.A = 0

1.A = A

A.A = A

A.Ā = 0

Question 5

Algebraic Boolean properties
Commutative
Associative
Distributive

Answer 5

Commutative:
A.B = B.A
A+B = B+A

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

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

Question 6

1) A.B + Ā.B
2) Ā + B.Ā
3) Ā . (A + B)
4) B. (A + A.B)
5) (A + A) . (A + B)

Answer 6

1) B
2) Ā
3) Ā.B
4) A.B
5) A

Question 7

Simple way to remember De Morgan’s Law

Answer 7

Break the line; change the sign

Question 8

What is the order of precedence

Answer 8

B.N.A.O
Brackets, Not, And, Or

Question 9

How to simplify Boolean algebra

Answer 9

1. Identify any NOR or NAND
2. Use De Morgan’s’ law