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1 Number System

Pre-Processing
Pre-Processing
• Types of Number System
• Conversion of Decimal Number into Binary Number
• Binary Addition • Binary Subtraction
• Binary Multiplication • Binary Division

A number system defines a set of values used to represent different quantities. It is essential for
manipulating and storing data on a computer.
Every number system uses one or more digits and has a base. The Base or Radix of a number system
is equal to the number of digits used in it. Numbers are formed by combining one or more digits.

Each digit in a number has two values: Face value and Place value.
(a) The face value of a digit in a number is the digit itself. For example, in the number 427, the face
value of the digit 7 is 7, the digit 2 is 2, and the digit 4 is 4.

(b) The place value of a digit depends on its place or position in the number. For example, in the
number 427, the digit 7 is at one’s place, so its place value is 7 × 1 = 7. The digit 2 is at ten’s place,
so its place value is 2 × 10 = 20. The digit 4 is at hundred’s place, so its place value is 4 × 100 = 400.
TYPES OF NUMBER SYSTEM
The four commonly used number systems are:

• Decimal Number System
• Binary Number System
• Octal Number System
• Hexadecimal Number System

Decimal Number System (Base 10)
We use the Decimal number system in our everyday work. It uses ten different symbols or digits
to represent values. So, the base of the Decimal number system is 10. The set values used in the
decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In the Decimal number system, each place
represents a power of 10.
Powers of Ten

6 Position 5 Position 4 Position 3 Position 2 Position 1 Position
th
th
nd
st
rd
th
100000 10000 1000 100 10 1
10 5 10 4 10 3 10 2 10 1 10 0
Ten to the Ten to the Ten to the Ten to the Ten to the Ten to the
power five power four power three power two power one power zero

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