NUMBER LOGIC / JD · 2026.10.19
Powers of Two: Doubling, Bits, and Useful Benchmarks
Learn the sequence from 2⁰ upward and why it appears in computing.
Doubling builds the powers
2⁰ = 1, 2¹ = 2, 2² = 4 and each next power doubles the previous one. Values through 2¹⁰ = 1,024 are practical checkpoints for recognizing binary sizes.
Powers versus multiples
A multiple of 2 is not necessarily a power of 2. For instance 12 is divisible by 2 but lies between 8 and 16. A positive power of 2 has exactly one 1 in its binary expansion.
Why computers care
Bits form base-two place values, making powers of two natural when describing address spaces and binary representations. Storage vendors may use decimal prefixes for capacity, so distinguish 1,000 from 1,024.
A quick activity
List the powers of two up to 2,048. For each value, write the binary notation, then compare with the neighboring integers to see how carrying works.