## Binary - Octal & Hexadecimal 1-15 Conversion Table

Decimal | Binary | Octal | Hexa-Decimal |

0 | 0 | 0 | 0 |

1 | 1 | 1 | 1 |

2 | 10 | 2 | 2 |

3 | 11 | 3 | 3 |

4 | 100 | 4 | 4 |

5 | 101 | 5 | 5 |

6 | 110 | 6 | 6 |

7 | 111 | 7 | 7 |

8 | 1000 | 10 | 8 |

9 | 1001 | 11 | 9 |

10 | 1010 | 12 | A |

11 | 1011 | 13 | B |

12 | 1100 | 14 | C |

13 | 1101 | 15 | D |

14 | 1110 | 16 | E |

15 | 1111 | 17 | F |

## How to Convert Decimal to Binary

To convert a decimal number to binary, we can do this by dividing the decimal number by 2 until the quotient is 0. The remainder of the division result is the binary number of the decimal number. For example, to convert 12310, we first do the division as follows:

Divided by 2 | Quotient | remaining quotient |
---|---|---|

123/2 | 61 | 1 |

61/2 | 30 | 1 |

30/2 | 15 | 0 |

15/2 | 7 | 1 |

7/2 | 3 | 1 |

3/2 | 1 | 1 |

1/2 | 0 | 1 |

After the quotient is equal to 0, the division is complete. To find the conversion result for 123_{10}, sort the remainder of the divider you get from the division from bottom to top. So that the conversion result of 123_{10} into binary is 1111011_{2}

## How to convert binary to decimal

To convert a binary number to decimal, we can do this by multiplying each bit in the binary number by 2^{n}, then the product is added up. An example of converting 1111011_{2} into decimal is as follows:

Binary | Multiplication | Multiplication Result |
---|---|---|

1 | 1 * 2^{6} | 64 |

1 | 1 * 2^{5} | 32 |

1 | 1 * 2^{4} | 16 |

1 | 1 * 2^{3} | 8 |

0 | 0 * 2^{2} | 0 |

1 | 1 * 2^{1} | 2 |

1 | 1 * 2^{0} | 1 |

Total = 123 |

After multiplying and adding up, it can be seen that 1111011_{2} in decimal is 123^{10}

## Decimal to Hexadecimal Conversion

How to convert a decimal number to hexadecimal is similar to how to convert a decimal number to binary, except that the decimal number is divided by 16 and the result must be converted into hex digits. Here is a list of digits used in hexadecimal numbers:

Decimal | Hex |
---|---|

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 8 |

9 | 9 |

10 | A |

11 | B |

12 | C |

13 | D |

14 | E |

15 | F |

An example of converting the decimal number 123_{10} into hexadecimal is as follows:

Divided by 16 | Quotient | Remaining Quotient | Hex Digit |
---|---|---|---|

123/16 | 7 | 11 | B |

7/16 | 0 | 7 | 7 |

After the division is complete, sort the hex digits obtained from bottom to top. So that the conversion result from 123_{10} to hexadecimal is 7B_{16}

## Hexadecimal to Decimal

The method of converting a hexadecimal number to decimal is similar to the cohesion of binary numbers to decimal. Before division, convert all hex digits in a hexadecimal number into decimal then multiply by 16^{n}, then add up the product. An example of converting 7B_{16} into decimal is as follows:

Hexadecimal | Decimal | Multiplication | Result |
---|---|---|---|

7 | 7 | 7 * 16^{1} | 112 |

B | 11 | 11 * 16^{0} | 11 |

Jumlah = | 123 |

## Hexadecimal to Binary and Binary to Hexadecimal Conversion

To convert a hexadecimal number to binary, it can be done by first converting a hexadecimal number to a decimal number then converting the decimal number to binary number. Likewise, the conversion of binary numbers to hexadecimal, that is, first convert binary numbers to decimal and then convert the decimal numbers into hexadecimal.