Binary to Hexadecimal

The binary number system is widely used as a computer programming language. It uses only two digits, ‘0’ and ‘1,’ to process data and instructions in digital electronics. Each binary digit is referred to as a ‘bit’.

The word hexadecimal comes from the Greek word ‘hex’, meaning six, and the Latin word ‘decem’, meaning ten. As the name suggests, the hexadecimal number system is a base-16 system having 16 different symbols that represent numbers. These symbols include the numbers 0 - 9 and the letters A - F. The hexadecimal system compactly represents large binary numbers.

The conversion from the binary number system to the hexadecimal number system is essential for simplification. This is useful in computer programming and debugging, as it simplifies binary data and makes it easier to work with.

There are two methods for binary to hexadecimal conversion:
 

In this method, binary digits are grouped, and those groups are directly converted into a hexadecimal digit, using the following steps:

Step 1: Starting from the least significant bit, i.e., the bit on the right, group the bits in sets of 4.

Step 2: Convert each 4-bit group into its equivalent hexadecimal digit using the conversion table.

Step 3: Combine all the hexadecimal digits for the final conversion.

For example, convert 110101112 to hexadecimal.

Step 1: Group 
1101 0111 are two 4-digit groups

Step 2: Convert
1101 = D
0111 = 7

Step 3: Combine
D7₁₆

In this method, the binary digits are first converted into decimal or octal, then again to hexadecimal. Let us take an example to understand the steps of conversion.

Question: Convert 11010111₂ to hexadecimal using indirect conversion method.
To convert binary to decimal:

Step 1: Multiply each digit by 2 raised to position of the digit from left to right.

Step 2: Add all values to get the decimal conversion.
11010111₂​ =1×2⁷+1×2⁶+0×2⁵+1×2⁴+0×2³+1×2²+1×2¹+1×2⁰= 215

To convert a decimal to a hexadecimal 

Step 1: Divide the decimal number by 16

Step 2: Write the remainder in hexadecimal 

Step 3: Repeat the division until the quotient is zero

Step 4: read the reminders from bottom to top for final conversion.
215 ÷ 16 = 13 remainder 7⇒D7_16​

The binary-to-hexadecimal conversion table simplifies direct conversion by listing each 4-bit binary value alongside its corresponding hexadecimal equivalent.

• Leading zero: Leading zeros are extra zeros placed at the beginning (left side) of a binary number to ensure its length is a multiple of four. They facilitate easier conversion without altering the binary number's value.

• Base: The base of a number system indicates the total count of distinct digits it uses, starting from zero. Each number system has a unique base.

• Least Significant Bit (LSB): The Least Significant Bit (LSB) is the rightmost digit in a binary number. It holds the smallest value and serves as the starting point when grouping bits for conversion. It is the bit multiplied to 20.