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.

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.

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

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

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

**Instructions:**

- Start with any hexadecimal number,
- Represent each hexadecimal digit with the equivalent group of 4 binary digits (see conversion table above),
- Concatenate the resulting binary digits into a single number,
- Discard any insignificant leading zeros at the left ot the resulting binary number.

**Example #1: Convert hexadecimal 158 into binary**

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

Translate hexadecimal digits into binary 4-digit groups | 0001 0101 1000 |

Concatenate binary digit groups | 000101011000 |

Discard leading zeros | 101011000 |

Resulting binary number |
101011000 |

**Example #2: Convert hexadecimal 2019 into binary**

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

Translate hexadecimal digits into binary 4-digit groups | 0010 0000 0001 1001 |

Concatenate binary digit groups | 0010000000011001 |

Discard leading zeros | 10000000011001 |

Resulting binary number |
10000000011001 |

Convert binary to hexadecimal numbers.

Convert hexadecimal to binary numbers.

Learn how to manually convert numbers between binary and hexadecimal numbering systems.