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Hex to Octal Converter



Converting a Hexadecimal Number to Octal

Hexadecimal (hex) and octal are both numeral systems used in computing. The hexadecimal system (base-16) uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen. The octal system (base-8) uses eight symbols: 0-7. Converting a hexadecimal number to octal involves two main steps: first, converting the hex number to binary, and then converting the resulting binary number to octal.

Each hex digit corresponds to four binary digits (bits), while each octal digit corresponds to three binary digits. This means that a direct conversion from hex to octal involves converting the hex number to binary, and then regrouping the binary digits into sets of three to form the octal number.

For example, the hexadecimal number 1A3 can be converted to octal by first converting it to binary:

1 = 0001, A = 1010, 3 = 0011

The binary equivalent is 000110100011. Next, group the binary digits into sets of three, starting from the right:

001 101 000 011

Finally, convert each group to its corresponding octal digit:

001 = 1, 101 = 5, 000 = 0, 011 = 3

Thus, the octal equivalent of 1A3 is 1503.

Examples

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

1. Convert the hexadecimal number 1A3 to octal.

Answer

First, we identify the given number:

Given:

  • Hexadecimal: 1A3

Next, we convert the hex digits to their binary equivalents:

Steps:

  • 1 = 0001
  • A = 1010
  • 3 = 0011

The binary equivalent is 000110100011. We then group the binary digits into sets of three, starting from the right:

Steps:

  • 001 101 000 011

Finally, convert each group to its corresponding octal digit:

  • 001 = 1
  • 101 = 5
  • 000 = 0
  • 011 = 3

The final octal value is:

Octal Equivalent:

1503

Result:

∴ The octal equivalent of the hexadecimal number 1A3 is 1503.

2. Convert the hexadecimal number 2F to octal.

Answer

We start by identifying the number:

Given:

  • Hexadecimal: 2F

Next, we convert the hex digits to their binary equivalents:

Steps:

  • 2 = 0010
  • F = 1111

The binary equivalent is 00101111. We then group the binary digits into sets of three, starting from the right:

Steps:

  • 000 010 111

Finally, convert each group to its corresponding octal digit:

  • 000 = 0
  • 010 = 2
  • 111 = 7

The final octal value is:

Octal Equivalent:

027

Result:

∴ The octal equivalent of the hexadecimal number 2F is 027.

3. Determine the octal equivalent of the hexadecimal number B9.

Answer

First, we identify the given number:

Given:

  • Hexadecimal: B9

Next, we convert the hex digits to their binary equivalents:

Steps:

  • B = 1011
  • 9 = 1001

The binary equivalent is 10111001. We then group the binary digits into sets of three, starting from the right:

Steps:

  • 001 011 100 1

Finally, convert each group to its corresponding octal digit:

  • 001 = 1
  • 011 = 3
  • 100 = 4
  • 1 = 1 (with two leading zeros)

The final octal value is:

Octal Equivalent:

1341

Result:

∴ The octal equivalent of the hexadecimal number B9 is 1341.

4. Convert the hexadecimal number 7D to octal.

Answer

We start by identifying the number:

Given:

  • Hexadecimal: 7D

Next, we convert the hex digits to their binary equivalents:

Steps:

  • 7 = 0111
  • D = 1101

The binary equivalent is 01111101. We then group the binary digits into sets of three, starting from the right:

Steps:

  • 011 111 101

Finally, convert each group to its corresponding octal digit:

  • 011 = 3
  • 111 = 7
  • 101 = 5

The final octal value is:

Octal Equivalent:

375

Result:

∴ The octal equivalent of the hexadecimal number 7D is 375.