# Binary Numbers

Binary Numbers are those which are represented using base 2. The two digits that we use for representing numbers in binary system are 0 and 1. Applications of binary numbers can be found in many aspects of studies of sciences. The mathematical systems for representing the numbers are decimal system, octal system and hexadecimal system. In the decimal system we used to have 10 digits from 0 – 9 for representing the numbers. Similarly, for octal we the digits range from 0 – 7 and for hexadecimal representation we use digits from 0 – 9 and A – F for 10 – 15.

A binary number can be converted to any of the above mentioned number systems by using specific techniques. The operations like addition, subtraction, ORing, ANDing etc. are possible with the binary numbers. Let us see how the numbers are represented in binary system.

 Octal Binary 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111

Next for hexadecimal:

 Hexadecimal Binary 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 A 1010 B 1011 C 1100 D 1101 E 1110 F 1111

Next let us discuss the conversion of binary numbers to other numbers systems and vice – versa.

Example 1: Convert (122)10 = (?)2

Solution: For converting 122 to base 2 we need to divide the number by 2 and collect all the remainders in the reverse order. 122 /2; R = 0 then 61 /2; R = 1 then 30 /2; R = 0, 15 /2; R = 1, 7 /2; R = 1 then 3 /2; R = 1 then 1 /2; R = 1. Collecting the remainders in reverse order we get:
(122)10 = (1111010)2
This way we can convert other numbers into binary.

## Binary Number System

Numbers with base value 2 are known as binary numbers. They are represented using two digits i.e. 0 and 1. For example: 01011 represents (0 × 24) + (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20), they represent 0 + 8 + 0 + 2 ...Read More

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