# 32 - Underflow and Overflow

1. A CPU with a capacity of 8 bits has a capacity of up to 11111111 in binary. If one more bit was added there would be an ___________

rounding error

underflow error

absolute error

overflow error

2. An example of an 8-bit __________ occurs in the binary sum 11111111 + 1 (denary: 255 + 1).

overflow error

underflow error

rounding error

absolute error

3. If the total (sum) is a number bigger than 8 digits, the CPU drops the _________ digit as it cannot be stored anywhere.

rounding

overflow

underflow

second last

4. Fill in the blanks for the following excerpt relating to a type of error.
```_______ errors happen when the largest number that a
register can hold is exceeded. The number of bits that
it can handle is called the _______```

overflow / word size

underflow / word size

over flow / bit size

underflow / floating point mantissa

5. Most CPUs use a much bigger word size than 8 bits. Many PCs have a 64-bit CPU. A 64-bit CPU can handle numbers larger than _______________

18 quintillion

180 million

18,000

8 million

6. 16-bit integers can hold numbers in the range -32768...32767 . So what happens when you add 20000 to 20000?

underflow error

absolute error

overflow error

rounding error

7. Assume the smallest negative number we can hold is -8. We would get an __________error if we tried to store -15.

rounding error

underflow error

overflow error

absolute error

8. Read the following excerpt and fill in the blanks (what type of error is it?)
```The smallest positive number we can hold is when the mantissa is the
smallest positive number and the exponent is the largest negative number.
he smallest positive (normalised) mantissa is 01000 and the largest
negative exponent is 100 (-4 as a 2s complement number).

The smallest positive number we can hold is therefore 0.03125.
If we tried to hold 0.02234 for example, we would get an ____________________```

rounding error

None of the above, as this refers to a logical error

underflow error

overflow error

9. A calculation resulting in a number so small that the negative number used for the exponent is beyond the number of bits used for exponents is called __________________

None of the above, as this refers to a logical error

rounding error

overflow error

underflow error

10. This is an example of ______________. ( 7 bits for 32-bit integers, or exponents smaller than -64).

overflow error

underflow error

None of the above, as this refers to a logical error

rounding error