Binary to Hex Converter

This binary to hexadecimal conversion tool converts strings of 0s and 1s into a compact hexadecimal representation. Enter a binary number, leave the base as "binary" to display its equivalent hexadecimal value along with its decimal and octal representations.

Binary and hexadecimal are two of the most commonly used simplified representations for programmers. Binary numbers represent how computers actually store data while hexadecimal allows you to read that same data without having to look at a long series of numbers.

The key to connecting these two base systems is simple: four binary digits always correspond exactly to one hexadecimal digit. So a long string of binary characters is grouped together, reducing its length by a factor of four.

Binary and hexadecimal systems - two ways to represent the same number.

The binary system is a base-2 number system. It uses only two symbols: 0 and 1. The value of each digit is twice that of the digit to its right.

The hexadecimal system is also a base-16 number system. Since each digit requires sixteen different symbols, the digits 0 through 9 are used followed by the letters A, B, C, D, E and F to represent ten through fifteen respectively.

To distinguish between the two systems we use markers in the notation. The prefix 0b stands for binary numbers while the prefix 0x stands for hexadecimal numbers. So 0b1010 and 0xA represent the same value, written in two different ways.

A half-byte - four bits make up a hexadecimal number

A group of four bits is called a nibble and is half of an eight-bit byte. The four bits are counted from 0000 to 1111, or decimal 0 through 15, which is exactly the range of values for one hexadecimal digit.

Since 2 to the power of 4 is 16, every possible nibble without a remainder corresponds to exactly one hexadecimal symbol. This table shows the whole conversion process in full and it's worth memorizing.

How to convert a binary number to hexadecimal.

The conversion can be done manually in two steps and also the above calculator uses the same logic.

Step 1: Divide into foursomes, starting on the right.

Starting with the bit furthest to the right (the least significant bit), mark off positions by moving left and making groups of four. If there are not enough bits in the group furthest on the left, pad it out with leading zeros until it has four digits.

Take the binary number 1011010 for example. Splitting it up from the right, we get 101 1010. By adding a zero to the front of the first group, we get 0101 1010.

Step 2: Transformation and concatenation of groups.

Replace each nibble with the corresponding hexadecimal character according to the table above and write down these hexadecimal numbers in the same order. For 0101 1010: 0101 becomes 5, 1010 becomes A, so the result is 5A.

This method can be used for any length binary number. The binary number 1110001111011 grouped and padded with zeros gives 0001 1100 0111 1011. Converting each half-byte to hexadecimal gives 1, C, 7, B so the hexadecimal value is 1C7B.

How to convert a hexadecimal number to binary.

The conversion in the opposite direction can also be done mechanically. Replace each hexadecimal digit with its corresponding four-digit half-byte from the table and concatenate them while preserving order.

In hexadecimal F1, F is 1111 and 1 is 0001, so in binary F1 is 11110001. After conversion all leading zeros can be removed.

There is an important note about this tool: The input field is a numeric field and does not accept letters A through F. It reads binary, decimal or octal numbers and outputs hexadecimal. To convert a hexadecimal number to binary, use the table above and convert each digit individually. The text field where you can directly enter hexadecimal numbers (as mentioned below) will be added later.

Binary to hexadecimal conversion table:

Looking at these common values the regularity is immediately apparent. It also contains clear byte and word boundaries which are useful to programmers.

Why do we use hexadecimal and where do we encounter it?

The value of the hexadecimal system is its compactness. A single hexadecimal digit represents four bits of information. Since two hexadecimal digits can represent a full byte, values that would otherwise be represented by eight hard-to-read binary digits can be compressed into a more readable two-digit hexadecimal value like FF.

If you look closely, this compact representation is everywhere. Colors of websites and designs are often represented by hexadecimal groups like #FF8800 where each two-digit number represents a color channel with values ranging from 0 to 255.

Memory addresses and pointers in debuggers are often displayed as hexadecimal values, e.g. 0x7FFF. Network devices use hexadecimal MAC addresses, and hex editors show the bytes of an original file pairwise. Error codes, status codes, Unicode code points (such as U+00E9) and even data words in standards like ARINC 429 use hexadecimal for this reason.

Bits, half bytes and bytes:

A bit is either a 0 or a 1. Four bits make up a half-byte, which is one hexadecimal character, and eight bits make up a byte, which is two hexadecimal characters. The range of values is between 0 and 255, or between 00 and FF.

Stacking more bytes quickly increases the range of values. A value with 16 bits consists of four hexadecimal numbers and can be a maximum of 65,535. A value with 32 bits consists of eight hexadecimal numbers and exceeds four billion. With each additional bit, the range of values doubles.

Distinguish between binary and hexadecimal systems:

If a number only contains the digits 0 and 1 it could be binary but the most reliable indicator is the prefix. The prefix "0b" or the subscript "2" indicates binary numbers, while the prefix "0x" or the subscript "16" indicates hexadecimal numbers.

You can also tell by the digits themselves. If a letter from A to F appears, or if a number greater than 1 appears in a code that is clearly not decimal, then it's hexadecimal.