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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 ___________

  overflow error

  absolute error

  underflow error

  rounding error

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

  rounding error

  underflow error

  absolute error

  overflow error

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

  second last

  rounding

  overflow

  underflow

 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 _______

  underflow / word size

  underflow / floating point mantissa

  over flow / bit size

  overflow / word size

 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 _______________

  8 million

  180 million

  18,000

  18 quintillion

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

  rounding error

  absolute error

  overflow error

  underflow error

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

  underflow error

  overflow error

  absolute error

  rounding 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 ____________________

  underflow error

  rounding error

  overflow error

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

  rounding error

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

  underflow error

  overflow error

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

  rounding error

  overflow error

  underflow error

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


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