3. NUMBER SYSTEM
Is a method of expressing values, using a set of symbols in a
consistent manner.
Several number systems has been used in the past which can be
categorized into two (2): positional and non-positional number
systems.
5. POSITIONAL NUMBER SYSTEM
In a positional number system, the position the symbol occupies
determines the value it represents, thus, it is also often called the
PLACE VALUE system.
6. HOW DOES IT WORKS?
If number is represented as:
± 𝒔𝒏−𝟏 ⋯ 𝒔𝟏 𝒔𝟎 . 𝒔−𝟏 𝒔−𝟐 ⋯ 𝒃
Then it has the value of:
𝒗 = ± 𝒔𝒏−𝟏 × 𝒃𝒏−𝟏 + ⋯ + 𝒔𝟏 × 𝒃𝟏 + 𝒔𝟎 × 𝒃𝟎 + 𝒔−𝟏 × 𝒃−𝟏 + 𝒔−𝟐 × 𝒃−𝟐 + ⋯
17. HEXADECIMAL NUMBER SYSTEM
• Is a number system with the base of 16.
• It uses sixteen (16) unique symbols to represent values.
0 1 2 3 4 5 6 7 8 9 A B C D E F
18. 1. 𝑨𝟏𝟗𝟏𝟔
• n = 3, b = 16
• 𝐴 × 162 + 1 × 161 + 9 × 160
• 10 × 256 + 1 × 16 + 9 × 1
• 256 + 16 + 9
• So the equivalent decimal number is Two Hundred Eighty
Example 1.d - Hexadecimal Number System, Positional Values
21. START
Create an empty destination
(v).
Divide the source (s) by the
destination base (b).
Insert the remainder at the
destination (v).
STOP
The quotient becomes the
new source (s).
TRUE
FALSE
Condition: Is the quotient zero?
Given:
s = Source Number
b = Destination Base
Return:
v = Destination Value
Figure 1.a - Conversion from Decimal to any Base (Integral Part)
27. Example 1.g - Decimal to Hexadecimal Conversion (IntegralValues)
Convert the number 𝟏𝟐𝟔𝟏𝟎 to octal.
Results: 𝟏𝟐𝟔𝟏𝟎 = 𝟕𝑬𝟏𝟔
126
7
0
E
7
Source
Destination
28. START
Create an empty destination
(v).
Multiply the source (s) by the
destination base (b).
Insert the integral part at the
destination (v).
STOP
The fractional part becomes
the new source (s).
TRUE
FALSE
Condition: Is the fractional part zero?
Given:
s = Source Number
b = Destination Base
Return:
v = Destination Value
Figure 1.b - Conversion from Decimal to any Base (Fractional Part)
