# Conversion of Binary and Hexadecimal Number System: GIS and Maths (Especially for GATE-Geospatial 2022)

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There are many methods or techniques which can be used to convert numbers from one base to another. We will demonstrate here the following:

## Conversion of Binary to Hexadecimal

Since, the base of hexadecimal number system is 16; 4 bits are required to express any hexadecimal digit. Conversion from binary to hexadecimal number may be made by grouping the integer and fractional parts of the number separately into groups of 4 bits starting from the least-significant bit position and converting them into corresponding hexadecimal digits.

Any unfilled group (less than 4 bits) in the integer part is filled with 0s in the more significant bit positions and in the fractional part with 0s in the less significant bit positions.

#### Example

Position 8421

### Shortcut Method – Binary to Hexadecimal

Steps:

1. Divide the binary digits into groups of four (start form right)

2. Convert each group of four binary digits to one hexadecimal symbol.

#### Example

Binary number -

Calculating Hexadecimal Equivalent –

Step | Binary Number | Hexadecimal Number |

Step 1 | ||

Step 2 | ||

Step 3 |

Binary Number Hexadecimal Number

## Conversion of Hexadecimal to Binary

To conversion from hexadecimal to binary number may be done just by following the reverse process, i.e.. , by conversion of the individual hexadecimal digits into their corresponding 4-bit representation.

#### Example

### Shortcut Method – Hexadecimal to Binary

Steps:

1. Convert each hexadecimal digit to a 4 digit binary number

2. Combine all the resulting binary groups into a single binary number.

**Example** Hexadecimal Number -

Calculating Binary Equivalent –

Step | Hexadecimal Number | Binary Number |

Step 1 | ||

Step 2 | ||

Step 3 |

Hexadecimal Number Binary Number