3.6.5.1 Using Boolean Algebra. Flashcards

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1
Q

What does Boolean algebra concern?

A

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.

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2
Q

Define A, B, C etc in Boolean algebra.

A

An unknown Boolean value being represented by a letter

just like or in conventional algebra.

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3
Q

__

Outline A in Boolean algebra.

A

NOT A. An overline represents the NOT operation being

applied to what is below the line.

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4
Q

Outline A • B in Boolean algebra.

A

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

(multiplication) operation.

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5
Q

Outline AB in Boolean algebra.

A

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

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6
Q

Outline A + B in Boolean algebra.

A

A OR B, where an addition symbol represents the OR

operation.

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7
Q

Define the order of precedence.

A

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

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8
Q

Outline the order of precedence.

A

Highest
Brackets .

NOT .

AND .

OR .
Lowest

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9
Q

Define a Boolean identity.

A

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

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10
Q

Outline De Morgan’s law.

A

“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).

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11
Q

Example of De Morgan’s law:

A

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
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12
Q

Outline the distributive rules.

A

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

A • (B + C) = A • B + A • C

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