The Binary Shortcut: Why Powers of Two Work—and Where They Fail

This article transforms a seemingly magical algorithm into an intuitive understanding of fundamental number systems. By revealing that binary conversions with powers of two are essentially bit-shift operations—just as decimal point movements are 'free' with powers of ten—readers gain insight into the notorious 0.1 + 0.2 ≠ 0.3 floating-point precision issue and how embedded systems leverage this principle through fixed-point arithmetic.