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 and base two representation,
the integers 0, 1, 2, ... , 2N - 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).
-
(2N - 1) is represented by 1....1....1 (all 1's).
These facts are NOT always true for other representation schemes!
Know what scheme is 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?
Look at fact 3 in the list and think a bit.
Hint: Actually, you should think about a bit.