The conversion between binary numbers and octal numbers is very easy and straightforward task. Let's start.
Key Questions:
- Convert octal number into binary number
- Convert binary number into octal number
- Convert octal fractional number into binary fractional number
- Convert binary fractional number into octal fractional number
Octal numbers
|
00
|
01
|
02
|
03
|
04
|
05
|
06
|
07
|
Binary numbers
|
00
|
01
|
10
|
11
|
100
|
101
|
110
|
111
|
Binary to Octal Conversion:
Whenever converting from binary to octal, its easy, just make group of 3 bits. And convert each 3 bit group to its equivalent octal value. But why we make group of 3 bits? Because 3 bits number in binary the total values can be expressed are 2n or largest possible value for a 3 bit number is 2n-1=7. The total digits or unique symbols in base 8 (octal) syatem are 8.
For integers start making groups from right to left.
Example 01011101)2
010 011 101
⇖
Start making group of 3 bits from here
We have a 8 bit number. Start making group of 3 bits from right. You can make 2 groups easily. For 3rd 3 bit group we have to add extra 0. As shown above
For fractional part start making group from left to right.
Example 0.1111000111)2
0.111 100 011 100
⇗
Start making group of 3 bits from here
Example#01:110111011.11010)2=?)2
Making group of 3 bits
110 111 011 . 110 100
Binary number
|
110
|
111
|
011
|
.
|
110
|
100
|
Octal number
|
6
|
7
|
3
|
.
|
6
|
4
|
Answer 110111011.11010)2=673.64)8
Example#02: 101111001.010101)2
Making group of 3 bits
101 111 001.010 101
Binary number
|
101
|
111
|
001
|
.
|
010
|
101
|
Octal number
|
5
|
7
|
1
|
.
|
2
|
5
|
Answer 110111011.11010)2=571.25)8
Example#03: 1111110011111001)2=?)8
Making group of 3 bits
001 111 110 011 111 001
Note: add two zeros on the left in order to make group of 3 bits.
Binary number
|
001
|
111
|
110
|
011
|
111
|
001
|
Octal number
|
1
|
7
|
6
|
3
|
7
|
1
|
Answer 1111110011111001)2=176371)8
Octal to Binary Conversion:
The conversion method is to take individual octal digit and convert it in binary. Make sure convert in the way that each octal digit should represent in 3 bit binary group.
For example if
1)8 =001)2 right way
1)8 =1)2 wrong way
Note: this is wrong for this conversion technique only. Otherwise it is obviously the same.
1)8 =1)2
Example#01:673.64)8= ?)2
Represent each octal digit in 3 bit binary number.
Octal number
|
6
|
7
|
3
|
.
|
6
|
4
|
Binary number
|
110
|
111
|
011
|
.
|
110
|
100
|
Answer 673.64)8= 110111011.110100)2
Or 673.64)8= 110111011.1101)2
Note: you can remove the right most 0s that are unnecessary.
Example#02: 571.25)8= ?)2
Represent each octal digit in 3 bit binary number.
Octal number
|
5
|
7
|
1
|
.
|
2
|
5
|
Binary number
|
101
|
111
|
001
|
.
|
010
|
101
|
Answer 571.25)8= 101111001.010101)2
Example#03: 176371)8=?)2
Represent each octal digit in 3 bit binary number.
Octal number
|
1
|
7
|
6
|
3
|
7
|
1
|
Binary number
|
001
|
111
|
110
|
011
|
111
|
001
|
Answer 176371)8= 1111110011111001)2
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