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Binary Calculator
Add, subtract, multiply, or divide binary numbers.
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💡 Expert Tips
Binary Addition Shortcut
0+0=0, 0+1=1, 1+0=1, and here's the tricky one: 1+1=10 (that's binary 10, which equals decimal 2). When you get 1+1, write 0 and carry the 1. Just like decimal addition, but it carries at 2 instead of 10.
Why Computers Use Binary
Transistors (the building blocks of CPUs) have two states: on or off. Binary maps perfectly: 1=on, 0=off. Using decimal (0-9) would require each transistor to have 10 states, which is physically impossible with current technology.
Hex is Binary's Friend
Hexadecimal (base-16) is just shorthand for binary. Every hex digit represents exactly 4 binary digits. F (hex) = 1111 (binary). Programmers use hex because it's way more readable than long strings of 0s and 1s.
⚠️ Common Mistakes
Entering 2s or Higher
Binary only has 0 and 1. If you type "102" thinking it's a binary number, that's wrong - there's no "2" in binary. The calculator will reject it. Only use 0 and 1.
Forgetting Leading Zeros Don't Matter
0001 = 1. Leading zeros don't change the value (just like 007 = 7 in decimal). But trailing zeros DO matter: 10 ≠ 100. 10 (binary) = 2 (decimal), while 100 (binary) = 4 (decimal).
Confusing Bit Positions
In binary 1010, the rightmost bit is worth 1, then 2, then 4, then 8 (powers of 2). Read right to left for value. 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10 decimal.