# Hexadecimal Number System

#### Problem Statement

In the octal system, we have grouped every 3 bits of a binary number.

But on the computer, the memory allocation always happens in multiples of 4.

Like, 1 Byte (8 bits), 4 Byte (32 bits).

#### How can we easily handle computer memory address?

#### Solution - Hexadecimal Number System

In the hexadecimal number system, we group every 4 binary bits. So that we can easily represent computer memory addresses.

Possible values that can be formed using 4 bit is 15 (1111)_{2}.

Hexadecimal Number System = {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}.

Itâ€™s also called as base 16 number system.

Binary |
Decimal |
Hexadecimal |
---|---|---|

0000 |
0 |
0 |

0001 |
1 |
1 |

0010 |
2 |
2 |

0011 |
3 |
3 |

0100 |
4 |
4 |

0101 |
5 |
5 |

0110 |
6 |
6 |

0111 |
7 |
7 |

1000 |
8 |
8 |

1001 |
9 |
9 |

1010 |
10 |
A or a |

1011 |
11 |
B or b |

1100 |
12 |
C or c |

1101 |
13 |
D or d |

1110 |
14 |
E or e |

1111 |
15 |
F or f |

The hexadecimal number system will use letters A to F to represent numbers 10 to 15.

10-A,11-B,12-C,13-D,14-E,15-F

## Binary to Hexadecimal

Let's convert (10001101) _{2} into hexadecimal format.

Group every 4 binary bits from right to left.

Finally, combine the results.

(10001101) _{2}

(1000) (1101)

(1000) = (8)

(1101) = (13) ==> 13 -> D

(1000) (1101) = (8D)_{16}

#### Pictorial Explanation

If the number of bits is not multiples of 4. Add zeros before the binary number to make it perfect 4-bit group.

#### Example

(101010) _{2}

Here, the number of bits is 6. By adding two zeros before the binary number, we can make it multiples of 4.

Like,(00101010) _{2}.

## Hexadecimal to Binary

To convert the hexadecimal number into binary, we need to represent every hexadecimal digit into 4 binary bits.

Finally, combine the binary bits.

#### Example

Let's convert (FD) _{16} into binary numbers

(FD) _{16}

F= (1111)

D= (1101)

(FD) _{16} = (11111101) _{2}