01 - Boolean Algebra Introduction

 1. Boolean Algebra can be thought of as a system of mathematics based on logic that has its own set of rules or laws which are used to define and reduce Boolean expressions
The followng presentation (optional to watch) is from



 2. Read the following excerpt on Boolean Algebra and fill in the blanks.
A set of rules or Laws of Boolean Algebra expressions 
have been invented to help ______ the number of logic
gates needed to perform a particular logic operation
resulting in a list of functions or theorems known 
commonly as the Laws of Boolean Algebra





 3. The variables used in Boolean Algebra only have one of two possible values, a logic “0” and a logic “1”



 4. Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854)



 5. A few basic rules to keep in mind are listed in the following plain text. Fill in the blanks.
Rules to keep in mind

1. Variables used can have only two values. 
Binary 1 for HIGH and Binary 0 for LOW.

2. Complement of a variable is represented by an overbar (-).
*Check with your exam board for the appropriate notation. 
The complement of variable B is represented as B Bar. 
If B = 0 then B Bar = ____.

3. ORing of variables is represented by a plus (+) sign or
a 'V'. For example ORing of A, B, C is represented as 

4. Logical ANDing of two or more variables is represented 
by writing a dot between them such as A.B.C. Sometime the 
dot may be omitted e.g. ABC.

  0 / ABC

  1 / A + B + C

  0 / A + B + C

  1 / ABC

 6. In the following, fill in the blanks for 1, 2 and 3

  1 = AND; 2 = NOT; 3 = OR

  1 = AND; 2 = OR; 3 = NOT

  1 = OR; 2 = AND; 3 = NOT

  1 = NOT; 2 = OR; 3 = AND

 7. A law of Boolean algebra is also referred to as an ____________





 8. A Boolean expression is any expression that has a Boolean value. For example, the ________________________ are Boolean expressions.

  binary sequences: 1001 and 11111

  operators +, -, MOD and %

  comparisons 3 < 5, x < 5, x < y and Age < 16

  sums, 2+3+5 or 13+13

 9. The expression x < 5 will give the result _____ when the variable x contains a number less than 5





 10. Boolean Algebra Laws are used to

  make logic circuits more efficient by adding more circuitry to the mix

  make boolean expressions more complex

  make logic circuits work faster by establishing which additonal gates can be included

  simplify boolean expressions.

 11. Which of the following laws is NOT a valid boolean algebra law?
Laws of Boolean Algebra
Idempotent Law
Associative Law
Commutative Law
Convoluted Law
Distributive Law
Identity Law
Complement Law
Involution Law
DeMorgan's Law
Redundancy Laws

  Idempotent Law

  Absorption Law

  Involution Law

  Convoluted Law

 12. In this series we will be using the notation as provided on Use the site to plug in the expression and obtain the result for the following:
~A + ~B * B 

Use the following site to simply 
plug in the expression and obtain the answer 
for this question>>

  The boolean expression is reduced to A

  The boolean expression is reduced to ~A

  The boolean expression is reduced to ~B*A

  The boolean expression is reduced to B+~A

 13. What could the following expression be simplified to? (use the suggested site if you are yet to study simplification and this is just an introduction)
 ~(A * B) * (~A + B) * (~B + B)

  The boolean expression is reduced to ~B*A

  The boolean expression is reduced to A

  The boolean expression is reduced to B+~A

  The boolean expression is reduced to ~A

 14. The simpler the boolean expression, the less logic gates will be used



 15. Give the relationship that represents the dual of the Boolean property A + 1 = 1? (Note: * = AND, + = OR and ' = NOT)

  A = 0

  A * 0 = 0

  A * 1 = 1

  A * 1 = 1