Binary system

This is number system which is used to represent values in the digital environment. Here value of b=2

(11101.01)₂

=1*2⁴ + 1 *2³ + 1 * 2² + 0 *2¹ + 1 * 2⁰+ 0 *2^-1 + 1 * 2^-2

= (29.25)₁₀ so number given is equal to 29 in decimal.

Representing large values in binary system may be very cumbersome and also it’s very difficult to a human to work with such large values in binary as it require 3 to 4 time more digits than for decimal system for same value e.g. 1010111101110111₂.Hence the number systems like octal and hexadecimal systems are developed just to simplify this. Corresponding equivalents of the value above in octal and hexadecimal are 127567₈ and AF77₁₆  that are easier to read and remember for engineers and other technicians

The weights of the corresponding bits for binary system are as

However, any series of 1’s and 0’s is not binary number. Sometimes it may represent some other information like some binary codes as gray code, parity bit numbers etc

Binary number formats:

1. Bit: It is defined as smallest unit of data. Eg. 0, 1
2. Nibble: It is a combination of 4 bits Eg. 0000, 1010, 1000, 0100 etc
3. Byte: A byte is a combination of 8 bits Eg. 0010 1010—it has 2 nibbles
4. Word: it is defined as combination of 16 bits Eg. 0010 0011 0111 1111 – it has 4 nibbles or 2 bytes
5. Double word: It is defined as combination of 32 bits.Eg. 0010 0011 0111 1111 0010 0011 0111 1111 it has 8 nibbles or 4 bytes