The conversion between hexadecimal and binary number systems is an easy task. Let’s start.
Key Questions:
Convert binary numbers into hexadecimal numbers
Convert hexadecimal numbers into binary numbers
How to convert binary fractions into hexadecimal fractions
How to convert hexadecimal fractions into binary fractions
Hexadecimal numbers
00
01
02
03
04
05
06
07
Binary numbers
0000
0001
0010
1111
0100
0101
0110
0111
Hexadecimal numbers
08
09
0A
0B
0C
0D
0E
0F
Binary numbers
1000
1001
1010
1011
1100
1101
1110
1111
Binary to Hexadecimal Conversion Examples:
Whenever converting from binary to hexadecimal numbers, start making a group of 4 bits. But why do we use 4 bits? Because 4 bits represent 16 different values. For integers, start making a group of 4 from right to left.
Binary to hexadecimal conversion
Example: Convert into a hexadecimal number:11100111101)2
011100111101
The above binary number is an 11-bit number. You can make two 4-bit groups easily. Convert every 4 binary bits (from LSB or bit-0) to a hex digit. For the third group, add zero at the leftmost position. So three groups of four bits have been made, as shown above.
For fractional numbers, start making groups of 4 bits from left to right.
Example: 0.11100110111)2
0.111001101110
In the above fractional number, you can easily make two groups of 4 bits, starting from the left. For the third group of 4 bits, we have to add a zero at the rightmost position, as shown above.
Let’s solve some examples so that you understand the conversion method.
Example#01: 1111111111)2 = ?)16
Making a group of 4 bits
001111111111
Binary number
0011
1111
1111
Hexadecimal number
3
F
F
Answer (111111111)2 = 3FF)16Example#2: 110010111010.11111111)2=?)16
Making a group of 4 bits
110010111010.11111111
Binary number
1100
1011
1010
.
1111
1111
Hexadecimal number
C
B
A
.
F
F
Answer 110010111010.11111111)2=CBA.FF)16Example#03: 11001100110011.111000111)2= ?)16
Making a group of 4 bits
0011001100110011.111000111000
Adding two 0s on the leftmost side completes a group of four bits. Adding three 0s in the rightmost position will complete a group of four bits.
Binary number
0011
0011
0011
0011
.
1110
0011
1000
Hexadecimal number
3
3
3
3
.
E
3
8
Answer 11001100110011.111000111)2= 3333.E38)16
Hexadecimal to Binary Conversion Examples:
When converting from hexadecimal to binary, pick a single hexadecimal digit and convert it to an equivalent binary number. One thing you have to keep in mind is that binary numbers should be represented in 4-bit format. For example
1)16=0001)2 right way
1)16=1)2 wrong way
Note: This is wrong while using this technique. Otherwise, it is right.
1)16=1)2
