3.6.5.1 Using Boolean Algebra.

Question 1

What does Boolean algebra concern?

Answer 1

Boolean algebra concerns representing values with
letters and simplifying expressions. Boolean algebra uses the Boolean values TRUE and
FALSE which can be represented as 1 and 0 respectively.

Question 2

Define A, B, C etc in Boolean algebra.

Answer 2

An unknown Boolean value being represented by a letter

just like or in conventional algebra.

Question 3

__

Outline A in Boolean algebra.

Answer 3

NOT A. An overline represents the NOT operation being

applied to what is below the line.

Question 4

Outline A • B in Boolean algebra.

Answer 4

A AND B, said “A dot B” where a dot represents the AND

(multiplication) operation.

Question 5

Outline AB in Boolean algebra.

Answer 5

An alternative notation for A AND B. Just like in
Mathematics, the product of two algebraic values can be
represented without any symbol.

Question 6

Outline A + B in Boolean algebra.

Answer 6

A OR B, where an addition symbol represents the OR

operation.

Question 7

Define the order of precedence.

Answer 7

Algebraic operations have an order of precedence, meaning that some operations must be
applied before others. Similar to BODMAS in maths.

Question 8

Outline the order of precedence.

Answer 8

Highest
Brackets .

NOT .

AND .

OR .
Lowest

Question 9

Define a Boolean identity.

Answer 9

There are a number of useful identities which can be used to simplify Boolean
expressions.

Question 10

Outline De Morgan’s law.

Answer 10

“break the bar and change the sign.”
Where “the bar” refers to an overline representing the NOT operation and “the sign” refers
to changing between + (OR) and • (AND).

Question 11

Example of De Morgan’s law:

Answer 11

For example, the Boolean expression can have De Morgan’s law applied to it as A + B
follows:

Break the bar:
_ _
A + B

Change the sign:
_   _
A • B
\_\_\_\_     _    _
A + B =  A • B 

De Morgan’s law can also be applied in reverse, by changing the sign and building the bar.

For example, the Boolean
_ _
expression C + D can be simplified as follows:

Change the sign:
_ _
C • D

Build the bar:
_    _
C • D
_    _     _   _
C + D = C • D

Question 12

Outline the distributive rules.

Answer 12

Just like expanding brackets in Mathematics, you can use distributive rules in Boolean
algebra as follows:

A • (B + C) = A • B + A • C