Binary system uses only 2 symbols, which are typically expressed as 0 (zero) and 1 (one). It has a positional notation and each digit is referred to as a single bit. All this makes it perfect for digital electronic circuitry and logic gates which means that binary system is used by almost all modern computers and similar devices.

Hexadecimal system is probably more familiar as a numeral system that is also commonly used by computers and other digital systems. It is base 16 and it has 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F.

**Table #1: Binary to hexadecimal conversion table**

Binary | 0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |

Hexadecimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |

**Instructions:**

- Start with any binary number,
- Divide it into groups of 4 digits (nibbles) by using the least significant bit at the right of the number as a starting point,
- Pad the first group of digits on the left with 0 (zeros) if there are less than 4 digits,
- Convert each group of 4 binary digits to its equivalent hexadecimal value (see conversion table above),
- Concatenate the resulting hexadecimal digits into a single resulting number.

**Example #1: Convert binary 101011000 into hexadecimal**

Step description | Result |
---|---|

Form groups of 4 binary digits | 1 0101 1000 |

Pad the first group with zeros | 0001 0101 1000 |

Translate binary groups into hexadecimal digits | 1 5 8 |

Resulting hexadecimal number |
158 |

**Example #2: Convert binary 10000000011001 into hexadecimal**

Step description | Result |
---|---|

Form groups of 4 binary digits | 10 0000 0001 1001 |

Pad the first group with zeros | 0010 0000 0001 1001 |

Translate binary groups into hexadecimal digits | 2 0 1 9 |

Resulting hexadecimal number |
2019 |

Convert binary to hexadecimal numbers.

Convert hexadecimal to binary numbers.

Explore the manual conversion process between hexadecimal and binary numbering systems.