3.6.5.1 Using Boolean Algebra. Flashcards
What does Boolean algebra concern?
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.
Define A, B, C etc in Boolean algebra.
An unknown Boolean value being represented by a letter
just like or in conventional algebra.
__
Outline A in Boolean algebra.
NOT A. An overline represents the NOT operation being
applied to what is below the line.
Outline A • B in Boolean algebra.
A AND B, said “A dot B” where a dot represents the AND
(multiplication) operation.
Outline AB in Boolean algebra.
An alternative notation for A AND B. Just like in
Mathematics, the product of two algebraic values can be
represented without any symbol.
Outline A + B in Boolean algebra.
A OR B, where an addition symbol represents the OR
operation.
Define the order of precedence.
Algebraic operations have an order of precedence, meaning that some operations must be
applied before others. Similar to BODMAS in maths.
Outline the order of precedence.
Highest
Brackets .
NOT .
AND .
OR .
Lowest
Define a Boolean identity.
There are a number of useful identities which can be used to simplify Boolean
expressions.
Outline De Morgan’s law.
“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).
Example of De Morgan’s law:
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
Outline the distributive rules.
Just like expanding brackets in Mathematics, you can use distributive rules in Boolean
algebra as follows:
A • (B + C) = A • B + A • C