Page 11 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes 4. A digital system is a combination of devices designed to manipulate physical quantities
or information that are represented in digital form; that is, they can take on only discrete
values.
(a) True (b) False

1.3 Hexadecimal Number System

The hexadecimal number system is used as an intermediary system in computers, such as are
presentation of memory addresses or a representation of colours. The hexadecimal number system
is also known as the base-16 number system, because each position in the number represents an
incremental number with a base of 16 (see Table 1.1). For example, the first position (the furthest
right) is represented as 16, the second position (one from furthest right) is represented as 16, and
so forth. To determine what the actual number is in “decimal” representation, take the number
that appears in the position, and multiply it by 16x, where x is the power representation. For
example, if a number appears in the furthest right position, take the number in the furthest right
position and multiply it by 16. If there are multiple positions in the number (ex: 17AF), add all
the results together.
Since the number system is represented in “sixteens”, there are only 10 numbers and 5 letters that
can be a value in each position of the base-16 number. Below are the numbers that each position
can hold:

Table 1.1: Comparing Number Hexadecimal to Decimal Values

Hexadecimal “Decimal Value”
Representation
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
A 10
B 11
C 12
D 13
E 14
F 15

Be careful to use ten different symbols like: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 for
hexadecimal number.

1.4 Octal Number System

Just as the decimal system with its ten digits is a base-ten system, the octal number system with its
8 digits, ‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’ and ‘7’, is a base-eight system. Table 1.2 shows the weighting for

6 LOVELY PROFESSIONAL UNIVERSITY