Binary Calculator Formula & How It Works
Decimal to Binary: divide by 2, collect remainders | Binary to Decimal: Σ(bit × 2ⁿ)
- Binary (base 2): digits 0 and 1
- Each bit position = power of 2 (rightmost = 2⁰=1)
- 1101₂ = 1×8 + 1×4 + 0×2 + 1×1 = 13₁₀
- Binary addition: 0+0=0, 0+1=1, 1+1=10 (carry 1)
Binary is the language of computers — all data is stored as 0s and 1s (bits). Converting decimal to binary: divide repeatedly by 2 and read remainders bottom-to-top. Binary arithmetic uses the same rules as decimal but only 0 and 1 are valid — any sum ≥ 2 carries to the next position.