My first instinct was to say 'false, it's way more than 2x' which is correct, but then I fumbled the actual explanation.
Start by stating that the statement is false, then explain that the number of values doubles with each additional bit, so a 64-bit integer represents 2^32 times more values than a 32-bit integer, not 2 times. Use the formula 2^n for n-bit integers and contrast the magnitudes to highlight the exponential growth.
Pro tip: Emphasize that the number of values doubles per bit, so the ratio between 64-bit and 32-bit is 2^32, which is about 4 billion—a common pitfall is to think linearly. This shows you understand exponential scaling, a key concept in systems design.
Restate the question to ensure understanding: 'The claim is that a 64-bit integer can represent roughly two times more values than a 32-bit integer.'
State that an n-bit integer can represent 2^n distinct values (assuming unsigned; for signed, it's also 2^n values, just with a different range).
Calculate: 32-bit gives 2^32 ≈ 4.29 billion values; 64-bit gives 2^64 ≈ 1.84×10^19 values.
Find the ratio: (2^64) / (2^32) = 2^32 ≈ 4.29 billion. So a 64-bit integer represents about 4 billion times more values, not 2 times.
Conclude the statement is false, and explain that the number of values doubles with each additional bit, leading to exponential growth.
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