Unsigned Integer Range by Bit Width

Unsigned Integer Range by Bit Width

1. Use the bit-width rule
   An unsigned integer with n bits can represent all whole numbers from 0 up to the largest value made by setting every bit to 1.

2. Find the maximum value
   The largest unsigned value is: [ 2^n - 1 ] because there are (2^n) total bit patterns, starting at 0.

3. Write the range clearly
   The full range is: [ 0 \text{ to } 2^n - 1 ] If the problem gives a specific number of bits, substitute it directly and simplify.

4. Check your answer
   Make sure the smallest value is 0 and the count of values is exactly 2^n. A quick check is that the range should include both endpoints and have no negative numbers.

Example method

If the width is 8 bits, compute (2^8 - 1 = 255), so the range is (0) to (255).

Common mistake to avoid

Do not use a negative starting value. Unsigned integers never represent negatives.