Binary to HEX

Binary System

The binary numeral system uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only two numbers: 0 and 1. 

While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world. This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.

Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 2⁰. In the binary system, each binary digit refers to 1 bit.

Hexadecimal System (Hex System)

The hexadecimal system (shortly hex), uses the number 16 as its base (radix). As a base-16 numeral system, it uses 16 symbols. These are the 10 decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the first six letters of the English alphabet (A, B, C, D, E, F). The letters are used because of the need to represent the values 10, 11, 12, 13, 14 and 15 each in one single symbol.

Hex is used in mathematics and information technologies as a more friendly way to represent binary numbers. Each hex digit represents four binary digits; therefore, hex is a language to write binary in an abbreviated form.

Four binary digits (also called nibbles) make up half a byte. This means one byte can carry binary values from 0000 0000 to 1111 1111. In hex, these can be represented in a friendlier fashion, ranging from 00 to FF.

In html programming, colors can be represented by a 6-digit hexadecimal number: FFFFFF represents white whereas 000000 represents black.

How to Convert Binary to Hex

Converting from binary to hex is easy since hexadecimal numbers are simplified versions of binary strings. You just need to remember that each hex digit represents four binary digits. It follows that four binary digits will be equal to one hex digit. The method is easier than it sounds but it’s always useful to use a binary to hex conversion chart to save time.

Step 1: Write down the binary number and group the digits (0’s and 1’s) in sets of four. Start doing this from the right. If the leftmost group doesn’t have enough digits to make up a set of four, add extra 0’s to make a group.

Step 2: Write 8, 4, 2 and 1 below each group. These are the weights of the positions or place holders in the number (2³, 2², 2¹ and 2⁰).

Step 3: Every group of four in binary will give you one digit in hexadecimal. Multiply the 8, 4, 2 and 1’s by the digit above. 

Step 4: Add the products within each set of four. Write the sums below the groups they belong to.

Step 5: The digits you get from the sums in each group will give you the hexadecimal number, from left to right.