Binary Converter

Convert between decimal, binary, and hexadecimal number systems

How Binary Conversion Works

Understanding number system conversions

Converting Decimal to Binary

To convert a decimal number to binary:

  1. Divide the decimal number by 2.
  2. Get the integer quotient for the next iteration.
  3. Get the remainder for the binary digit.
  4. Repeat the steps until the quotient becomes 0.
  5. The binary equivalent is the sequence of remainders read from bottom to top.

Example: Converting 25 to Binary

25 ÷ 2 = 12 remainder 1

12 ÷ 2 = 6 remainder 0

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Binary result (reading remainders from bottom to top):

11001

Hexadecimal Conversion

Hexadecimal (base-16) uses digits 0-9 and letters A-F (where A=10, B=11, ..., F=15). It's commonly used in computing as a more concise way to represent binary data, where each hex digit represents 4 binary digits.

Binary 1010 1101 = Hex AD (because 1010 = A and 1101 = D)

About Binary Numbers

Understanding binary and its applications

Binary is a base-2 number system that uses only two digits: 0 and 1. It's the fundamental language of computers and digital systems.

In binary, each position represents a power of 2, starting from the rightmost digit (2⁰ = 1) and increasing as you move left (2¹ = 2, 2² = 4, 2³ = 8, etc.).

Binary is essential in computing because electronic components can easily represent two states: on/off, high/low voltage, or magnetized/demagnetized.

Number Systems

  • Decimal (Base-10):0-9
  • Binary (Base-2):0-1
  • Octal (Base-8):0-7
  • Hexadecimal (Base-16):0-9, A-F

Common Binary Values

Decimal
Binary
Hex
0
0
0
1
1
1
2
10
2
5
101
5
10
1010
A
16
10000
10
255
11111111
FF