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
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06
|
07
|
Binary numbers
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0000
|
0001
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0010
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1111
|
0100
|
0101
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0110
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0111
|
Hexadecimal numbers
|
08
|
09
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0A
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0B
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0C
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0D
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0E
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0F
|
Binary numbers
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1000
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1001
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1010
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1011
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1100
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1101
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1110
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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
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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
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A
|
.
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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
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1000
|
Hexadecimal number
|
3
|
3
|
3
|
3
|
.
|
E
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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
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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
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