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Decimal to Octal Converter



Converting a Decimal Number to Octal

The octal number system, also known as base-8, is a numeral system that uses eight distinct digits: 0 to 7. Octal numbers are used in computing and digital systems, particularly in environments where binary or hexadecimal representations might be too lengthy or complex. Each digit in an octal number represents three binary digits (bits), which makes it easier to interpret certain binary data.

To convert a decimal number (base 10) to octal (base 8), we repeatedly divide the number by 8, recording the remainder at each step. The octal equivalent is obtained by reading the remainders in reverse order, starting from the last division.

Examples

Let’s explore some examples to understand how to convert decimal numbers to their octal equivalents.

1. Convert the decimal number 85 to octal.

Answer

First, we identify the given number:

Given:

  • Decimal: 85

Next, we divide the number by 8, recording the quotient and remainder at each step:

Steps:

  • 85 ÷ 8 = 10, remainder = 5
  • 10 ÷ 8 = 1, remainder = 2
  • 1 ÷ 8 = 0, remainder = 1

We then read the remainders from bottom to top:

Octal Equivalent:

125

Result:

∴ The octal equivalent of the decimal number 85 is 125.

2. Convert the decimal number 64 to octal.

Answer

We start by identifying the number:

Given:

  • Decimal: 64

Next, we divide the number by 8, recording the quotient and remainder at each step:

Steps:

  • 64 ÷ 8 = 8, remainder = 0
  • 8 ÷ 8 = 1, remainder = 0
  • 1 ÷ 8 = 0, remainder = 1

We then read the remainders from bottom to top:

Octal Equivalent:

100

Result:

∴ The octal equivalent of the decimal number 64 is 100.

3. Determine the octal equivalent of the decimal number 128.

Answer

First, we identify the given number:

Given:

  • Decimal: 128

Next, we divide the number by 8, recording the quotient and remainder at each step:

Steps:

  • 128 ÷ 8 = 16, remainder = 0
  • 16 ÷ 8 = 2, remainder = 0
  • 2 ÷ 8 = 0, remainder = 2

We then read the remainders from bottom to top:

Octal Equivalent:

200

Result:

∴ The octal equivalent of the decimal number 128 is 200.

4. Convert the decimal number 255 to octal.

Answer

We start by identifying the number:

Given:

  • Decimal: 255

Next, we divide the number by 8, recording the quotient and remainder at each step:

Steps:

  • 255 ÷ 8 = 31, remainder = 7
  • 31 ÷ 8 = 3, remainder = 7
  • 3 ÷ 8 = 0, remainder = 3

We then read the remainders from bottom to top:

Octal Equivalent:

377

Result:

∴ The octal equivalent of the decimal number 255 is 377.