# Binary Numbers

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. BIT is a contraction of the world’s BInary digiT.

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.

• 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
• Diminished Radix Complement
• Arithmetic Operations of Binary Numbers