Binary to Decimal Conversion: A Complete Beginner's Guide

What is Binary?

Binary is a base-2 number system that uses only two digits: 0 and 1. While humans count in base 10 (using digits 0–9), computers use binary because electronic circuits can easily represent two states: on (1) and off (0).

How to Convert Binary to Decimal

Each position in a binary number represents a power of 2, starting from the right (2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8, and so on). To convert, multiply each digit by its position value and add them all up.

Example: 1011 in binary

• 1 × 2^3 = 8
• 0 × 2^2 = 0
• 1 × 2^1 = 2
• 1 × 2^0 = 1
• Total: 8 + 0 + 2 + 1 = 11 in decimal

How to Convert Decimal to Binary

Divide the number by 2 repeatedly and record the remainders. Read the remainders from bottom to top.

Example: 13 in decimal

• 13 ÷ 2 = 6 remainder 1
• 6 ÷ 2 = 3 remainder 0
• 3 ÷ 2 = 1 remainder 1
• 1 ÷ 2 = 0 remainder 1
• Read bottom to top: 1101

Common Binary Values to Memorize

• 0000 = 0    0001 = 1    0010 = 2    0011 = 3
• 0100 = 4    0101 = 5    0110 = 6    0111 = 7
• 1000 = 8    1001 = 9    1010 = 10    1111 = 15
• 11111111 = 255 (8 bits / 1 byte max)

Use our free binary converter to convert between decimal, binary, hex and octal instantly.

Step-by-Step Conversion Examples

Understanding IPv4 Addresses in Binary

Every IP address on the internet is stored as four 8-bit binary numbers. The address 192.168.1.1 breaks down as:

• 192 = 11000000 in binary (128+64 = 192)
• 168 = 10101000 in binary (128+32+8 = 168)
• 1 = 00000001
• 1 = 00000001

Each octet must stay within 0–255 because that's the maximum value of 8 bits (2⁸ − 1 = 255). This is why IP addresses can never contain a number above 255 — it would require more than one byte. A /24 subnet mask (255.255.255.0) = 11111111.11111111.11111111.00000000 in binary.

ASCII: How Text is Stored as Binary

Every character you type is stored as a binary number. In ASCII encoding:

• The letter "A" = 65 decimal = 01000001 binary
• The letter "a" = 97 decimal = 01100001 binary
• The digit "0" = 48 decimal = 00110000 binary
• A space = 32 decimal = 00100000 binary

Verification: 01000001 = 0+64+0+0+0+0+0+1 = 65 = "A" ✓

The difference between uppercase "A" (65) and lowercase "a" (97) is exactly 32 — the value of bit 5. Toggling bit 5 switches between upper and lowercase for any ASCII letter. Modern systems use UTF-8, which is backward-compatible with ASCII for all characters below 128.

Converting a 16-Bit Value

In computing, 16-bit values are common — integers, audio samples, port numbers. Let's convert binary 1100101000111110 to decimal:

• Group into nibbles: 1100 / 1010 / 0011 / 1110
• Active bits (left to right): 2¹⁵, 2¹⁴, 2¹⁰, 2⁹, 2⁵, 2⁴, 2³, 2², 2¹
• = 32768 + 16384 + 1024 + 512 + 32 + 16 + 8 + 4 + 2 = 50,750 decimal

This same value is representable as 0xCA3E in hexadecimal (C=12, A=10, 3=3, E=14) — one hex digit per 4 bits. This is why programmers prefer hex for reading binary values larger than one byte.

Negative Numbers: Two's Complement

CPUs don't store negative numbers as "minus sign + value." They use two's complement: flip all bits, then add 1. For −13 in 8-bit signed representation:

• Start with +13 = 00001101
• Flip all bits (one's complement): 11110010
• Add 1: 11110011
• Result: 11110011 = −13 in two's complement

Verification: 11110011 as unsigned = 128+64+32+16+2+1 = 243. As signed: 243 − 256 = −13 ✓

This is why signed 8-bit integers range from −128 to +127, not 0–255. The highest bit acts as the sign bit: 0 = positive, 1 = negative. A signed 8-bit −128 = 10000000 has no positive equivalent within the same range (128 doesn't fit), making it an asymmetric range.

Source: IEEE 754 floating-point standard; Unicode Consortium UTF-8 specification. Last verified: May 2026.