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Octal to Binary Converter



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Converting an Octal Number to Binary

The octal numeral system (base-8) uses digits from 0 to 7. In computing, octal numbers are sometimes used because they can represent binary numbers more compactly. Each octal digit corresponds to exactly three binary digits (bits), making the conversion from octal to binary straightforward and efficient.

To convert an octal number to its binary equivalent, each octal digit is replaced with its corresponding 3-bit binary value. This ensures that the resulting binary number accurately represents the original octal number.

For example, the octal number 345 can be converted to binary by converting each digit individually:

3 = 011, 4 = 100, 5 = 101

Therefore, the binary equivalent of 345 is 011100101.

Examples

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

1. Convert the octal number 345 to binary.

Answer

First, we identify the given number:

Given:

  • Octal: 345

Next, we convert each octal digit to its corresponding 3-bit binary value:

Steps:

  • 3 = 011
  • 4 = 100
  • 5 = 101

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

011100101

Result:

∴ The binary equivalent of the octal number 345 is 011100101.

2. Convert the octal number 52 to binary.

Answer

We start by identifying the number:

Given:

  • Octal: 52

Next, we convert each octal digit to its corresponding 3-bit binary value:

Steps:

  • 5 = 101
  • 2 = 010

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

101010

Result:

∴ The binary equivalent of the octal number 52 is 101010.

3. Determine the binary equivalent of the octal number 701.

Answer

First, we identify the given number:

Given:

  • Octal: 701

Next, we convert each octal digit to its corresponding 3-bit binary value:

Steps:

  • 7 = 111
  • 0 = 000
  • 1 = 001

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

111000001

Result:

∴ The binary equivalent of the octal number 701 is 111000001.

4. Convert the octal number 16 to binary.

Answer

We start by identifying the number:

Given:

  • Octal: 16

Next, we convert each octal digit to its corresponding 3-bit binary value:

Steps:

  • 1 = 001
  • 6 = 110

The final binary value is formed by concatenating these binary digits:

Binary Equivalent:

001110

Result:

∴ The binary equivalent of the octal number 16 is 001110.