How to Convert Binary, Octal, Decimal, and Hexadecimal with Calculation Examples and Quick Reference Tables

Easy-to-understand explanation of base-N conversion methods essential for programming and IT exams. We also include the conversion procedure from binary to hexadecimal and a convenient quick reference table.

Basics of Radix Conversion (Base-N)

The numbers we normally use are "decimal (using 10 digits from 0 to 9)", but in the computer world, "binary (using only 0 and 1)" is used. Furthermore, to make binary easier for humans to handle, it is often expressed collectively as "octal" or "hexadecimal".

Binary: Expressed in 0s and 1s. (Example: 1010)
Octal: Expressed from 0 to 7. (Example: 12)
Decimal: Expressed from 0 to 9. (Example: 10)
Hexadecimal: Expressed from 0 to 9 and A to F. (Example: A)

Simple Conversion Procedure from Binary to Hexadecimal

To convert a binary number to hexadecimal, the easiest way is to divide the binary number into groups of "4 digits from the right" and convert them. This is because 2 to the power of 4 is 16, and 4 binary digits correspond exactly to 1 hexadecimal digit.

Example: Convert the binary number "11010110" to hexadecimal
1. Divide into groups of 4 digits: 1101 and 0110
2. Convert each to decimal: 1101 = 13, 0110 = 6
3. Replace with hexadecimal: 13 is "D", 6 is "6"
Result: D6

Frequently Asked Questions

Q. Why is hexadecimal frequently used in programming?

A. Because binary numbers processed by computers have long digits and are hard for humans to read, hexadecimal (Hex), which can represent a 4-digit binary number as a single character, is ideal for expressing color codes and memory addresses.

Q. How do you calculate the conversion from decimal to binary?

A. You can convert a decimal number to binary by continuously dividing the decimal number by 2 and lining up the "remainders" in order from bottom to top.