Question

What is the minimum number of bits needed to give a binary encoding for 17 items?

Answer 1

Answer:

minimum numbers of bits needed is 8

Answer 2

Minimum number of bits needed to give a binary encoding for 17 items-5 bits

Explanation

• With n bits, we can make $2^n$ combinations.

• Simply, 4 bits gives you $2\times2\times2\times2$ = 16 encoding options, and 5 bits gives you $2\times2\times2\times2\times2$ = 32 encoding options.
• However, if two items are a fair bit rarer, then you can encode the first 15 items straightforwardly, leaving a special code like 0000 free to extend to the next 16 items. This will be a bit closer to 4 bits per item, depending on relative proportions.
• A bit is an electronic switch that can be ON or OFF, making 2 possible combinations.
• A byte consist of 8 bits, good for $2^8$ = 256 combinations, exactly the number of characters in the ASCII table.

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