Binary to Decimal Guide: How to Convert Between Number Systems

What Is the Binary Number System?

Binary (base-2) is a number system that uses only two digits: 0 and 1. It is the foundation of all digital computing because electronic circuits have two natural states: on (1) and off (0). Every piece of data your computer processes — text, images, video, software — is ultimately represented as a sequence of binary digits (bits).

In contrast, the decimal (base-10) system uses digits 0–9 and is the system humans use in everyday life.

How Binary Works

In decimal, each digit's position represents a power of 10 (ones, tens, hundreds...). In binary, each position represents a power of 2:

Position:    7    6    5    4    3    2    1    0
Value:      128   64   32   16    8    4    2    1

The binary number 10110101 means:

1×128 + 0×64 + 1×32 + 1×16 + 0×8 + 1×4 + 0×2 + 1×1 = 181

Binary to Decimal Conversion

Step-by-Step Method

1. Write down the binary number.
2. Assign powers of 2 to each position, starting from the right with 2⁰.
3. Multiply each binary digit by its corresponding power of 2.
4. Add all the results together.

Example: Convert 1101 to decimal

1×8 + 1×4 + 0×2 + 1×1 = 8 + 4 + 0 + 1 = 13

Decimal to Binary Conversion

Division Method

1. Divide the decimal number by 2.
2. Write down the remainder (0 or 1).
3. Divide the quotient by 2 again.
4. Repeat until the quotient is 0.
5. Read the remainders from bottom to top.

Example: Convert 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
Result: 11001

Common Binary Values

Decimal	Binary	Decimal	Binary
0	0	16	10000
1	1	32	100000
2	10	64	1000000
4	100	128	10000000
8	1000	255	11111111
10	1010	256	100000000

Related Number Systems

• Octal (base-8): uses digits 0–7. Each octal digit maps to exactly 3 binary digits. Used in Unix file permissions.
• Hexadecimal (base-16): uses 0–9 and A–F. Each hex digit maps to exactly 4 binary digits. Widely used for colors (#FF5733), memory addresses, and MAC addresses.

Convert between all bases using our Number Base Converter.

Why Binary Matters

Even if you never need to convert binary by hand in your daily life, understanding binary is essential for:

• Computer science and programming fundamentals
• Networking (IP addresses, subnet masks)
• Understanding file sizes (a byte is 8 bits = 2⁸ = 256 values)
• Bitwise operations in programming

Conclusion

Binary is the language of computers, and converting between binary and decimal is a fundamental skill for anyone studying technology. Use our Decimal to Binary converter for instant, accurate conversions.