The conversion between binary numbers and octal numbers is an effortless and straightforward task. Let’s start.
Key Questions:
- Convert octal numbers into binary numbers
- Convert binary numbers into octal numbers
- Convert octal fractional numbers into binary fractional numbers
- Convert binary fractional numbers into octal fractional numbers
| Octal numbers | 00 | 01 | 02 | 03 | 04 | 05 | 06 | 07 |
|---|---|---|---|---|---|---|---|---|
| Binary numbers | 00 | 01 | 10 | 11 | 100 | 101 | 110 | 111 |
Binary to Octal Conversion:
The conversion method is to make a group of three bits. But why do we make a 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) system are 8.
For integers start making groups from right to left.
Example 01011101)2
010 011 101
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
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= ?)10
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