Binary, Decimal, Hexadecimal and Octal Converter with Step-by-Step Solution

About Number Base Conversion

Convert from/to decimal, hexadecimal, octal, and binary. Decimal Base Conversion Calculator. Here you can find the answer to questions like Convert 10 decimal to binary or Decimal to binary conversion.

How to Convert Between Number Bases

Binary to Decimal

To convert binary to decimal, multiply each digit by 2 raised to its position power (starting from 0 on the right), then sum all the results.

Example: 1010₂ = 1 x 2³ + 0 x 2² + 1 x 2¹ + 0 x 2⁰ = 8 + 0 + 2 + 0 = 10₁₀

Decimal to Binary

To convert decimal to binary, repeatedly divide by 2 and record the remainders. Read the remainders from bottom to top.

Example: 10 / 2 = 5 (remainder 0), 5 / 2 = 2 (remainder 1), 2 / 2 = 1 (remainder 0), 1 / 2 = 0 (remainder 1). Reading remainders bottom-to-top: 1010₂

Decimal to Hexadecimal

Divide by 16 repeatedly and record remainders (0-9 and A-F for 10-15).

Hexadecimal to Decimal

Multiply each digit by 16 raised to its position power, then sum all results.

Decimal, Binary, Hexa and Octal Chart Table

When to Use Different Number Systems

Binary (Base 2) in Computing

Computers use binary because electronic circuits have two states: on (1) and off (0). Every piece of data in your computer - text, images, videos - is ultimately stored as binary numbers. Understanding binary helps programmers debug low-level code and work with bitwise operations.

Octal (Base 8) in Unix/Linux

Octal numbers are commonly used for Unix file permissions. The permission value 755 (rwxr-xr-x) means the owner has read, write, and execute permissions, while group and others have read and execute only. Each octal digit represents three binary bits, making it compact for permission representation.

Hexadecimal (Base 16) in Programming

Hexadecimal is the preferred format for representing memory addresses, color codes (#FF5733), and byte values. Two hex digits represent exactly one byte (8 bits), making it more readable than binary. Web developers use hex colors daily, and programmers see hex values in debuggers and memory dumps.

Common Important Values

• 255 (decimal) = FF (hex) = 11111111 (binary) - Maximum value for one byte, used in RGB color values
• 256 (decimal) = 100 (hex) = 100000000 (binary) - Number of possible values in one byte (0-255)
• 64 (decimal) = 40 (hex) = 1000000 (binary) - 2⁶, commonly used in encoding (Base64)
• 128 (decimal) = 80 (hex) = 10000000 (binary) - 2⁷, number of ASCII characters

References:

• SI Units - National Institute of Standards and Technology (NIST)
• IEEE Standards Association - Institute of Electrical and Electronics Engineers
• Bits and Binary - Khan Academy
• Computation Structures - MIT OpenCourseWare