Octal to Hex Converter

What Is the Octal Number System?

The octal number system uses base 8 and eight digits, from 0 to 7. Each digit has a place value based on powers of 8. Octal also links neatly to binary because one octal digit equals three binary bits, which makes base conversion quick.

What Is Hexadecimal?

Hexadecimal is a base 16 number system. It uses digits 0 to 9 and letters A to F. Each hex digit represents four binary bits. This compact form helps students read computer values, memory data, and programming values more easily.

How to Convert Octal to Hex Manually

Binary works as a bridge because an octal digit equals three binary bits. Group it into four bits, then map each group to hex.

Formula

$1\ octal\ digit = 3\ binary\ bits$

$1\ hexadecimal\ digit = 4\ binary\ bits$

Step by step Guide

1. Write the octal number.
2. Change each digit into three binary bits.
3. Group binary digits into four.
4. Add leading zeros if needed.
5. Map each group to hex.

Practical Example

$345_8$: $3=011$, $4=100$, $5=101$.

$345_8 = 011100101_2$

Group: $0000\ 1110\ 0101_2$.

$1110=E$, $0101=5$, so $345_8 = E5_{16}$.

Octal to Hex conversion table

Note: Each octal digit becomes three binary bits. Group the full binary value into four bits, then match each group to one hexadecimal digit.

Why Use Binary as an Intermediate?

Binary makes octal to hex conversion easier because $8=2^3$ and $16=2^4$. Each octal digit maps to three bits. Each hex digit maps to four bits. Regrouping connects both systems without difficult arithmetic. This method reduces long calculations.