Binary Converter
Convert between decimal and binary number systems instantly. Perfect for students, programmers, and anyone learning computer science fundamentals.
255 in decimal = 11111111 in binary
What Is the Binary Number System?
The binary number system (base-2) uses only two digits — 0 and 1 — to represent all numeric values. Every computer, smartphone, and digital device stores and processes information in binary because transistors have two stable states: on (1) and off (0). Understanding binary is essential for computer science, programming, digital electronics, and networking.
In contrast, the decimal system (base-10) that humans use every day has ten digits (0–9). Converting between these two systems is a foundational skill for anyone working with low-level programming, bitwise operations, IP addresses, or memory addresses.
Decimal to Binary Reference Table (0–15)
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 0 | 0 | 8 | 1000 |
| 1 | 1 | 9 | 1001 |
| 2 | 10 | 10 | 1010 |
| 3 | 11 | 11 | 1011 |
| 4 | 100 | 12 | 1100 |
| 5 | 101 | 13 | 1101 |
| 6 | 110 | 14 | 1110 |
| 7 | 111 | 15 | 1111 |
Frequently Asked Questions
What is binary?▼
Binary is a base-2 number system using only the digits 0 and 1. It is the fundamental language of computers because electronic circuits can represent two states — on (1) and off (0).
How do you convert decimal to binary?▼
Divide the decimal number by 2 repeatedly, recording the remainder each time, then read the remainders from bottom to top. For example, 13 → 1101 in binary.
How do you convert binary to decimal?▼
Multiply each binary digit by 2 raised to its positional power (starting at 0 from the right), then sum all values. For 1101: (1×8)+(1×4)+(0×2)+(1×1) = 13.
What is hexadecimal and how does it relate to binary?▼
Hexadecimal (base-16) uses digits 0–9 and letters A–F. Each hex digit maps exactly to 4 binary bits, making hex a compact shorthand for binary — widely used in color codes, memory addresses, and machine code.