Hex to Binary Converter

1. Conversion of hex numbers to binary numbers
2. How to convert hex to binary
3. Hexadecimal to binary conversion table

    Conversion of hex numbers to binary numbers

Both hexadecimal (hex, base 16) numbers and binary (bits, base 2) numbers see heavy usage in computer architecture, software engineering and related computer science disciplines. Since computers are electrical machines, they represent data in binary "bits" wherein 0 is recorded with a lack of electrical voltage and 1 is represented by its presence, making the binary system with its two numbers: ones and zeroes, the natural mathematical choice.

The hex system of number representation is convenient since binary numbers translate nicely to hex numbers translate nicely to binary ones, while the latter a much easier to read and remember. This was especially important in the early days of computing when a lot of programming was performed manually, e.g. via assembler instructions. Its importance has since been limited mostly to software engineers working with languages of low levels of abstractions, although hex appears in high-level markup languages and protocols as well, e.g. entity references in html and URL characters in the HTTP protocol.

Conversion from hex to binary numbers can be given as an exam task or home assignment in order to test the understanding of these two systems in students of various computer science courses.

    How to convert hex to binary

First, write down the hex number by replacing each digit by its binary equivalent from the reference table below. Add insignificant leading zeroes if the binary number has less than 4 digits, e.g. write 11₂ (3 decimal) as 0011₂. Finally, concatenate the groups of 4 binary digits together.

Example 1: Convert the hex number e7 to binary.

Solution: e₁₆ = 1110₂, 7₁₆ = 0111₂. Concatenating 1110 and 0111 we get the answer: 11100111.

    Hexadecimal to binary conversion table

If you decide to manually perform the conversion this table can be a useful reference:

Note how aa is exactly 1010 (a) concatenated with itself, bb is 1011 (b) concatenated with itself. This and other properties make conversion between hex and binary very convenient, even by hand.