Competition problem — Combinatorics

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Combinatorics Difficulty 4.2 AIME Find the answer United States

Problem:
A computer program is a function that takes in 4 bits, where each bit is either a $0$ or a $1$ , and outputs TRUE or FALSE. How many computer programs are there?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
The function has $2^{4}$ inputs and $2$ outputs for each possible input, so the answer is $2^{2^{4}} = 2^{16} = 65536$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.