Page 19 - Handout Digital Electronics

LECTURE 3 NUMBER SYSTEMS
1.1 Introduction
A number system defines a set of values used to represent quantity. We talk about the number of
people attending class, the number of modules taken per student, and use numbers to represent
grades achieved by students in tests. Quantifying values and items in relation to each other is helpful
for us to make sense of our environment. The study of number systems is not just limited to
computers. We apply numbers every day and knowing how numbers work will give us an insight into
how a computer manipulates and stores numbers.

1.2 Base Values
The base value of a number system is the number of different values the set has before repeating
itself. For example, decimals have a base of ten values, 0 to 9.

Decimal = 10 (0 - 9)

Binary = 2 (0, 1)

Octal = 8 (0 - 7)

Hexadecimal = 16 (0 - 9, A-F)

We will limit ourselves to the above number base systems due to their usage in computing.

1.3 Decimal Number System (Base 10)
This number base system is also called denary system and is the most common to us as human beings
as we use it in our daily lives to do calculations and counting. It uses ten (10) different symbols to
represent values. The set values used in decimal are 0 1 2 3 4 5 6 7 8 9 and 0 has the least value and
nine has the greatest value. The digit on the left has the greatest value, whilst the digit on the right has
the least value. To count in base ten, you go from 0 to 9, and then do combinations of two digits
starting with 10 all the way to 99. To count in base ten, you go from 0 to 9, then do combinations of
two digits starting with 10 all the way to 99 After 99 comes three-digit combinations from 100 – 999,
etc. This combination system is true for any base you use. The only difference is how many digits you
have before you go to the next combination

Although this is the most common number base system in use in our daily lives, computers do not use
this base for representing data/information.

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