Answer:

2⁸ - 1 = 256 - 1 = 255.

There are 256 patterns possible with 8 bits. But when these patterns represent integers, One of the patterns (0000 0000) is used for zero.

Largest Positive Integer in N Bits

The representation scheme we are looking at is called unsigned binary because no negative numbers are represented. Often when people say "binary number" this is what they mean. Here are some of its characteristics:

With N bits, the integers 0, 1, 2, ... , 2^N - 1 can be represented.
- So, for instance, with 8 bits, the integers 0, 1, ..., 2⁸ - 1 can be represented. This is 0 ... 255.

With N bits, zero is represented by 0....0....0 (all 0's).

(2^N - 1) is represented by 1....1....1 (all 1's).

These facts are NOT always true for other representation schemes! Know what scheme is being used before you decide what a pattern represents.

QUESTION 6:

Without doing any calculation, which of the following is the decimal equivalent of 1111 1111 1111?

2048
4095
16384
18432

Look at fact 3 in the list and think a bit.

Hint: Actually, you should think about a bit.