Number Conversion - Binary to Octal and Octal to Binary



UpdatedUpdatedJune 04 - 2017June 04 - 2017

Binary to Octal:

Using the knowledge that we have gained from the previous lessons, we first convert the binary number into decimal, and later we convert the decimal into octal number.


Shortcut method - binary to octal:

Let's first develop a chart containing all binary octal representations.

BinaryOctal
0000
0011
0102
0113
1004
1015
1106
1117



Now we will use this chart to convert the numbers easily.


Binary (base-2) to octal (base-8) conversion:
Step 1: From right (LSD or least significant digit) to left (MSD or most significant digit), divide the binary digits into groups of three.
Step 2: Convert each group of three binary digits into one octal digit.
Step 3: Combine all the resulting octal digits into a single octal number.


Example:

Binary number: 11011102
Or, 001 101 1102
StepBinaryOctal
111011102---
20012 1012 110218 58 68
3110111021568
So, the octal representation: 1568


Octal to Binary:

Using the knowledge that we have gained from the previous lessons, we first convert the octal number into decimal, and later we convert the decimal into binary number.


Shortcut method - octal to binary:


Octal (base-8) to Binary (base-2) conversion:
Step 1: From left (MSD or most significant digit) to right (LSD or least significant digit), convert each octal digit into a 3-digit binary number.
Step 2: Combine all the resulting binary digits into a single binary number.


Example:

Octal number: 1568
StepOctalBinary
115680012 1012 1102
2156811011102
So, the binary representation: 11011102