Binary To Octal Converter

Binary To Octal Converter

Binary to Octal converter is used to convert the binary number into the octal number (from the base-2 system to the base-8 system) and also convert the octal to binary by hitting on the swap button.

What is a Binary number system?

Binary number system is based on the “2” and contains only two numbers “0 and 1”. Due to this is also called a base-2 numeral system. Each number of the binary number system is known as a binary number that is a combination of the “0 or 1” and makes a small/large binary string.

In binary numbers, each digit is known as the binary digit while in computer language each binary digit is named as the bit. Bit plays an important role in programming and computer languages. A binary number in mathematical form can be represented as “(a)2”.

Where,

• “a” represents the binary digit.

What is octal number system?

Octal number system is based on the “8” and contains the eight elements from “0 to 7”. Due to this is also named as the base-8 numeral system. It contains a fewer element than the decimal and hexadecimal number system.

In computer language, an octal number is used to shorten the representation of the binary number into a group of three binary digits. The mathematical representation of the Octal number such as “(b)8”.

Where,

• “b” represents the octal number (i.e., 17, 476, and 7676).

How to convert the binary number into an octal number?

To convert the binary into an octal number first convert the binary to decimal number and decimal to octal. Follow the below steps to convert the binary number into an octal number.

• First, convert the binary to decimal to note the placement value from right to left, and place it in the exponent of “2” with the multiple of its digit. Also, placement values start from zero to move from right to left.
• Factorize the decimal with the number “8” to convert it into the octal number.

Here, we solve some manual examples to convert binary to octal and you can cross-match the results with the above binary to octal converter.

Example 1

Convert the given binary number into the octal number “11011011”.

Solution

Step 1: First convert the given binary number into a decimal number by using the placement value in the exponent of “2”.

(11011011)₂  = (1 × 2⁷) + (1 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)

          = (1 × 128) + (1 × 64) + (0 × 32) + (1 × 16) + (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)

By simply and adding all values get the decimal number.

          = (128) + (64) + (0) + (16) + (8) + (0) + (2) + (1)
          = 219

Step 2: Now, the above decimal number is converted into an octal number to factorize by “8”.

Thus, (11011011)2 = (333)8

Example 2

Convert the given binary number into the octal number “10111101”.

Solution

Step 1: First convert the given binary number into a decimal number by using the placement value in the exponent of “2”.

(10111101)₂  = (1 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)

          = (1 × 128) + (0 × 64) + (1 × 32) + (1 × 16) + (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1)

By simply and adding all values get the decimal number.

          = (128) + (0) + (32) + (16) + (8) + (4) + (0) + (1)
          = 189

Step 2: Now, the above decimal number is converted into an octal number to factorize by “8”.

Thus, (10111101)2 = (275)8