Question

the apple iphone includes a settings menu where you can toggle various accessibility options on or off:
mono audio
phone noise cancellation
hearing aid compatibility
what is the minimum number of bits that can represent those 3 options?

Explanation:

Step1: Recall bit representation

A single bit can represent 2 states (0 or 1, off or on). The number of states \( N \) that can be represented with \( n \) bits is \( N = 2^n \).

Step2: Calculate for n=1,2,3

• For \( n = 1 \): \( 2^1 = 2 \) states (not enough for 3 options).
• For \( n = 2 \): \( 2^2 = 4 \) states (enough for 3 options, since \( 4 \geq 3 \)).

Answer:

2