🔢 Binary (Base 2)
🔟 Decimal (Base 10)
Enter a binary or decimal number above to see the conversion
⚡ Quick Examples
📊 Powers of 2 Reference
What Is Binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit is called a bit (short for "binary digit"). Computers use binary because their hardware — transistors — operates with two electrical states: on and off. All data a computer processes — text, images, audio, video — is stored and manipulated as sequences of bits.
In contrast, the decimal system (base 10) uses ten digits (0–9) and is what humans use in everyday life. Converting between binary and decimal is a foundational skill in computer science, networking, and digital electronics.
How to Convert Binary to Decimal
Each position in a binary number corresponds to a power of 2. The rightmost position is 2⁰ (which equals 1), the next is 2¹ (2), then 2² (4), 2³ (8), and so on. To convert binary to decimal, multiply each bit by its positional value and add the results.
Example: Convert binary 11010 to decimal
1 × 2⁴ = 16
1 × 2³ = 8
0 × 2² = 0
1 × 2¹ = 2
0 × 2⁰ = 0
Total: 16 + 8 + 0 + 2 + 0 = 26
How to Convert Decimal to Binary
Divide the decimal number by 2 repeatedly. At each step, record the remainder (0 or 1). Continue until the quotient reaches 0. Then read the remainders from bottom to top — that sequence is the binary representation.
Example: Convert decimal 26 to binary
26 ÷ 2 = 13, remainder 0
13 ÷ 2 = 6, remainder 1
6 ÷ 2 = 3, remainder 0
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1
Read bottom → top: 11010
How Many Values Can N Bits Represent?
A group of N bits can represent 2N distinct values, ranging from 0 to 2N − 1.
| Bits | Values | Range | Common Name |
|---|---|---|---|
| 4 | 16 | 0–15 | Nibble (one hex digit) |
| 8 | 256 | 0–255 | Byte |
| 16 | 65,536 | 0–65,535 | Short / Word |
| 32 | 4,294,967,296 | 0–4,294,967,295 | Int / IPv4 address space |
Where Binary Is Used
- Computing: All CPU operations — arithmetic, logic, memory access — happen in binary
- Networking: IP addresses and subnet masks are 32-bit binary numbers (e.g., 255.255.255.0 = 11111111.11111111.11111111.00000000)
- File permissions: Unix/Linux chmod values map to 3-bit binary groups (e.g., 755 → 111 101 101)
- Color codes: Each RGB channel uses 8 bits, so
#FF0000means red = 11111111, green = 00000000, blue = 00000000 - Data storage: File sizes are measured in bytes (8 bits), kilobytes (2¹⁰ bytes), megabytes (2²⁰ bytes), and so on
Common Mistakes When Converting
- Reading the wrong direction: When dividing to get binary, read remainders bottom-to-top, not top-to-bottom
- Forgetting zeros: The 0 bits matter —
101(5) is different from11(3) - Confusing bit count with value: An 8-bit number is not 8; it can represent values from 0 to 255
- Mixing up signed and unsigned: In signed binary (two's complement), the leftmost bit indicates negative.
11111111is 255 unsigned, but −1 as a signed 8-bit integer
For a broader guide covering binary, decimal, and hexadecimal systems, see Understanding Number Systems: Binary, Decimal, and Hexadecimal.
Frequently Asked Questions
How do you convert binary to decimal?
Multiply each binary digit by its positional power of 2, then add the results. Starting from the rightmost digit, positions represent 2⁰ (1), 2¹ (2), 2² (4), 2³ (8), and so on. For example, binary 1101 = (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1) = 13 in decimal.
What is binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit is called a bit. Computers use binary because electronic circuits have two states: on (1) and off (0). All data in a computer — text, images, video — is ultimately stored and processed as binary.
How do you convert decimal to binary?
Divide the decimal number by 2 repeatedly and record the remainder at each step. Continue until the quotient is 0. Then read the remainders from bottom to top. For example, 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading bottom-to-top gives 1101.
What is 11111111 in decimal?
Binary 11111111 equals 255 in decimal. This is the maximum value that fits in one byte (8 bits): 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This value appears frequently in networking (subnet masks), color codes (max channel value in RGB), and file permissions.
Why do computers use binary?
Computers use binary because their hardware is built from transistors — tiny electronic switches with two states: on and off. Representing data with just two states is more reliable and energy-efficient than using circuits with ten states. Binary also maps directly to Boolean logic (true/false), which is the foundation of all digital circuits.
How many decimal values can N bits represent?
N bits can represent 2N different values, ranging from 0 to 2N − 1. For example: 8 bits → 256 values (0–255), 16 bits → 65,536 values (0–65,535), 32 bits → 4,294,967,296 values (0–4,294,967,295).
What is the difference between binary and hexadecimal?
Binary (base 2) uses digits 0 and 1. Hexadecimal (base 16) uses digits 0–9 and letters A–F. Hex is a compact shorthand for binary because each hex digit maps to exactly 4 binary digits. For example, hex FF = binary 11111111 = decimal 255. Programmers use hex for readability when working with binary data like memory addresses and color codes.
Is this binary to decimal converter free?
Yes. This converter is completely free with no sign-up required. All conversion happens locally in your browser — no data is sent to any server. You can convert binary to decimal and decimal to binary, toggle individual bits interactively, and see a step-by-step breakdown of the calculation.
Privacy & Limitations
- All calculations run entirely in your browser -- nothing is sent to any server.
- Results are computed using standard formulas and should be verified for critical applications.
Related Tools
- Password Generator -- Generate secure random passwords
- Data Usage Cost Estimator -- Estimate monthly data usage and costs by activity type
- Screen Resolution Calculator -- Calculate PPI, aspect ratio, and display quality metrics for any screen size
- UUID Generator -- Generate random UUIDs instantly
Related Tools
View all toolsASCII Table
ASCII codes with decimal, hex, and character lookup
Decimal to Hex Converter
Convert decimal numbers to hexadecimal
UUID Generator
Generate random UUIDs instantly
Base Converter
Convert numbers between bases 2 and 36
Data Size Converter
Convert between bytes, KB, MB, GB, and TB
Binary File Size Calculator
Convert file sizes between decimal and binary units with bits/bytes support
Binary to Decimal Converter FAQ
How do you convert binary to decimal?
Multiply each binary digit by its positional power of 2, then add the results. Starting from the rightmost digit, positions represent 2⁰ (1), 2¹ (2), 2² (4), 2³ (8), and so on. For example, binary 1101 = (1×8) + (1×4) + (0×2) + (1×1) = 13 in decimal.
What is binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit is called a bit. Computers use binary because electronic circuits have two states: on (1) and off (0). All data in a computer — text, images, video — is ultimately stored and processed as binary.
How do you convert decimal to binary?
Divide the decimal number by 2 repeatedly and record the remainder at each step. Continue until the quotient is 0. Then read the remainders from bottom to top. For example, 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading bottom-to-top gives 1101.
What is 11111111 in decimal?
Binary 11111111 equals 255 in decimal. This is the maximum value that fits in one byte (8 bits). It is calculated as 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This value appears frequently in networking (subnet masks), color codes (max channel value in RGB), and file permissions.
Why do computers use binary?
Computers use binary because their hardware is built from transistors, which are tiny electronic switches with two states: on and off. Representing data with just two states (1 and 0) is more reliable and energy-efficient than using circuits with ten states. Binary also maps directly to Boolean logic (true/false), which is the foundation of digital circuits.
How many decimal values can N bits represent?
N bits can represent 2^N different values, ranging from 0 to 2^N − 1. For example, 8 bits represent 256 values (0–255), 16 bits represent 65,536 values (0–65,535), and 32 bits represent 4,294,967,296 values (0–4,294,967,295).
What is the difference between binary and hexadecimal?
Binary (base 2) uses digits 0 and 1. Hexadecimal (base 16) uses digits 0–9 and letters A–F. Hex is a compact way to write binary because each hex digit maps to exactly 4 binary digits. For example, hex FF = binary 11111111 = decimal 255. Programmers use hex for readability when working with binary data.
Is this binary to decimal converter free?
Yes. This converter is completely free with no sign-up required. All conversion happens locally in your browser — no data is sent to any server. You can convert binary to decimal and decimal to binary, toggle individual bits, and see step-by-step breakdowns.