Binary converter

Computers store everything — text, images, video, your bank balance — as sequences of 1s and 0s. This is because transistors, the basic building blocks of processors and memory, have two states: on (1) and off (0). Binary is the natural language of digital hardware. Understanding it helps when you're studying computer science, dealing with network addressing, doing low-level programming, or just satisfying curiosity about how devices actually work.

Each position in a binary number represents a power of 2, starting from 2⁰ = 1 on the right. The binary number 1011 means: 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11 in decimal.

To convert decimal to binary manually, repeatedly divide by 2 and record the remainders from right to left. 13 ÷ 2 = 6 r1, 6 ÷ 2 = 3 r0, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1. Read remainders from bottom to top: 1101. So 13 in decimal = 1101 in binary. This calculator does that instantly, but understanding the manual process helps it stick.

• Computer science coursework: Binary arithmetic, two's complement for negative numbers, bitwise operations.
• Networking: IP addresses and subnet masks are often expressed in binary to understand how they work.
• Digital electronics: Logic gate design, reading technical datasheets, understanding memory addressing.
• Color codes: RGB hex codes are just binary values for red, green, and blue channels expressed in hexadecimal shorthand.