# Octal to Binary

## System of octal numbers

The base-8 number system known as "oct," or just "oct," employs the digits 0 to 7 to represent numbers. By arranging a series of binary digits in groups of three, it is possible to create octal numerals (starting from the right).

## System of binary numbers:

A binary number is a number stated in the binary numeral system or base-2 numeral system, which commonly uses the symbols 0 (zero) and 1 to represent numerical values. Binary numbers are used in mathematics and digital technology (one). A positional notation with a radix of 2, the base-2 system. Almost all current computers and computer-based gadgets employ the binary system internally because to its simple implementation in digital electronic circuits using logic gates.

### Example

To convert octal 154_{8 }to binary, for instance:

154_{8} = 1 5 4 = 1 101 100 = 11011002

## How Can I Change From Octal To Binary?

It takes two steps to convert an octal number to a binary number. The given octal number must first be converted into its corresponding decimal number, which must then be converted into binary. Let's go over the entire process right now.

### Conversion of Octal to Decimal

Determine how many digits are included in the given number. Let n be the number of digits.

When a digit is in the nth place from the right end of the integer, multiply each digit by 8n-1. If there is a decimal part to the number, multiply each digit by "8-m" when it is in the mth position from the decimal point.

After multiplying the terms, add them all.

The calculated value is the corresponding decimal number.

### Decimal to binary Conversion

Divide the decimal number generated above by two.

List the remaining information.

Till the quotient is zero, repeat the previous two procedures for the quotient.

Reverse the order of the remaining sentences.

The received number corresponds to the specified octal number in binary.

### Example

Convert the number 10_{8 }to a binary format.

Solution

10_{8} = (1 * 81) + (0 * 80)

= 1 * 8 + 0 * 1

= 8 + 0

= 8 (Decimal number)

## Octal to Binary Converter

You must enter an octal value, such as 5332, into the field and then click the Convert button to use this octal to binary conversion. The converter will provide you with the provided octal's binary equivalent.

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