**In binary numbers
system first we will discuss about the;**

**Data** are a
collection of facts and figures which act as a raw material for information.
The processed data which help to make decisions or further manipulations are
called **information**.

The total number of symbols used in a particular number
system is called base or radix and each symbol is called a **digit**. The decimal number system has base 10 and the digits are 0,
1, 2, 3, 4, 5, 5, 6, 7, 8, 9.

To binary number system have base 2 and the binary digits 0 and 1.

**Electronic and
electrical components of a computer **are bistable in nature. The binary
digit 0 and 1 are most suitable and are conveniently used to express the two
possible status. Internal circuit designs of a computer become simplified as
the circuits have to handle only two bits instead of ten digits of the decimal
system. Also all the operations that can be done in decimal system can also is
done in binary system.

**Conversion of number**
from one system to another is necessary to understand the logic and process of
operations. Binary numbers can be easily converted to decimal numbers and vice
versa. **Conversion of binary numbers to
decimal numbers** can be conveniently accomplished by either actual expansion
method or by value box method. Similarly decimal numbers may be converted to
binary numbers either by value box method or by multiplication and division
method.

**Octal and hexadecimal
number systems** are also used in digital computers. Octal number system has
a base 8 and the symbols used are 0, 1, 2, 3, 4, 5, 6, 7. Hexadecimal number
system has a base 16 and the symbols used are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,
B, C, D, E, F. Conversion of binary numbers to octal or hexadecimal numbers and
vice versa can also be easily accomplished.

**Addition,
subtraction, multiplication and division of binary number system** can be
made by following the usual rules of arithmetic.

- Number System

- Decimal Number System

- Why Binary Numbers are Used

- Binary to Decimal Conversion

- Conversion of Numbers

- Hexa-decimal Number System

- Conversion of Binary Numbers to Octal or Hexa-decimal Numbers

- Octal and Hexa-Decimal Numbers

- Signed-magnitude Representation

- Radix Complement

- Diminished Radix Complement

- Arithmetic Operations of Binary Numbers

**Binary Addition****Binary Subtraction****Subtraction by 2’s Complement****Subtraction by 1’s Complement****Addition and Subtraction of Binary Numbers****Binary Addition using 1’s Complement****Binary Addition using 2’s Complement****Binary Multiplication****Binary Division****Addition and Subtraction of Octal Numbers****Multiplication of Octal Numbers****Hexadecimal Addition and Subtraction**

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