Hexadecimal to Binary and Binary to Hexadecimal Conversion Solved Examples

The conversion between hexadecimal and binary number system is easy and straightforward task. Let's start.

Key Questions:

• Convert binary numbers into hexadecimal numbers
• Convert hexadecimal numbers into binary numbers
• How to convert binary fraction into hexadecimal fraction
• How to convert hexadecimal fraction into binary fraction

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:

Whenever converting from binary to hexadecimal numbers, start with making group of 4 bits. But why we use 4 bits? Because  4 bits represent 16 different values. Or the largest possible value for 4 bit number is 2n-1. For integers start making group of 4 from right to left.

Example 11100111101)2

0111 0011 1101

The above binary number is an 11 bit number. You make two 4 bits groups easily. For third group add zero at the leftmost position. So 3 groups of 4 bits has been made as shown above.

For fractional numbers, start making groups of 4 bits from left to right.

Example: 0.11100110111)2

0.1110 0110 1110

In the above fractional number you can easily make two groups of 4 bits, starting from left. While for 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 the you understand the conversion method.

Convert the given binary number into hexadecimal number Example#01: 1111111111)2  = ?)16

Making group of 4 bits

0011 1111 1111

Binary number	0011	1111	1111
Hexadecimal number	3	F	F

Answer 1111111111)2  = 3FF)16

---

Convert the given binary number into hexadecimal number Example#2: 110010111010.11111111)2=?)16

Making group of 4 bits

1100 1011 1010.1111 1111

Binary number	1100	1011	1010	.	1111	1111
Hexadecimal number	C	B	A	.	F	F

Answer 110010111010.11111111)2=CBA.FF)16

---

 

Convert the given binary number into hexadecimal number  Example#03: 11001100110011.111000111)2= ?)16

Making group of 4 bits

0011 0011 0011 0011.1110 0011 1000

Adding two 0s on leftmost side to complete a group of 4 bits. Adding three 0s on rightmost position in order to complete a group of 4 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:

When converting from Hexadecimal to binary number pick a single hexadecimal digit and convert it to equivalent binary number. One thing you have to keep in mind that binary number should be represent 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 absolutely right.  

1)16=1)2

Convert the given hexadecimal number into binary number Example#01:3FF)16= ?)2

3)16=0011)2

Hexadecimal number	3	F	F
Binary number	0011	1111	1111

Answer 3FF)16= 001111111111)2

---

Convert the given hexadecimal number into binary number Example#02:CBA.FF)16= ?)2

Hexadecimal number	C	B	A	.	F	F
Binary number	1100	1011	1010	.	1111	1111

Answer CBA.FF)16= 110010111010.11111111)2

---

Convert the given hexadecimal number into binary number Example#03: 3333.E38)16= ?)2

Hexadecimal number	3	3	3	3	.	E	3	8
Binary number	0011	0011	0011	0011	.	1110	0011	1000

Answer 3333.E38)16= 11001100110011.111000111)2