Answer:

  11111 111
   0000 0001     1₁₀
   1111 1111   255₁₀
   0000 0000    00₁₀

The carry bit of 1 out of the high order column (leftmost) indicates an overflow (for 8-bit unsigned addition).

Negative Integers

Unsigned binary representation can not represent negative integers. With paper and pencil numbers, a number is made negative by putting a negative sign in front of it: 24₁₀ negated = -24₁₀. You might hope to do the same with binary integers:

0001 1000    negated =   -0001 1000  ???

Unfortunately, you can't put a negative sign in front of a bit pattern in computer memory. Memory holds only patterns of 0's and 1's. Somehow negative integers must be represented using bit patterns. This is certainly possible. Remember those advantages of binary?

Easy to build.
Unambiguous signals (hence noise immunity).
Can be copied flawlessly.
Anything that can be represented with symbols can be represented with patterns of bits.

If we can represent negative integers with paper and pencil (thus using symbols) we certainly can represent negative integers with patterns of bits.

QUESTION 11:

Let us say that you need to represent an equal number of positive and negative integers in eight bits. How many negative numbers can represented? How many positive numbers?

Just for fun, can you think of a way to do this? Get out some scratch paper and scratch for a while with eight-bit patterns.