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

(11101.01)_{2}

=1*2^{4 }+ 1 *2^{3} + 1 * 2^{2} + 0 *2^{1} + 1 * 2^{0}+ 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. 1010111101110111_{2}.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 127567_{8} and AF77_{16 }that are easier to read and remember for engineers and other technicians

The weights of the corresponding bits for binary system are as

2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} | . | 2^{-1} | 2^{-2} |

16 | 8 | 4 | 2 | 1 | . | 0.50 | 0.25 |

MSB | Decimal point |

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:**

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