Topic 1e
CFU Answers

Checking for Understanding

1. Which of these two error types is caused by a limit in the number of bits at the low end of the bit string?
• Running out of bits at the low (fractional) end of a numerical encoding is a truncation error.
2. Which of these two error types is caused by a limit in the number of bits at the high end of the bit string?
• Running out of bits at the high (integer) end of a numerical encoding is an overflow error.
3. Which of these two error types is most likely to occur when we add two bit strings together?
• When we add to values together we typically increase the value stored.
• Thus, we are likely to exceed the maximum value able to be stored by the bit-string.
• Thus, we have an overflow error.
4. Which of these two error types is most likely to occur when we attempt to encode a number like Pi into binary?
• Pi is a number that never terminates in the decimal portion of the number.
• Thus, we increasingly have smaller and smaller fractional values to encode
• Eventually, we run out of bits to encode these fractional values.
• Thus, we have a truncation error.
5. Which of these two error types is most likely to occur when we store decimal (base 10) numbers like money values in a binary encoding?
   • Fractional values in decimal are 1/10, 1/100, 1/1000, etc.
   • These don't always have good translations to fractional values in binary which are 1/2, 1/4, 1/8, 1/16, etc.
   • Thus, it is sometimes hard to take a particular value like 1/100 and convert it to a sum of fractional powers of 2. We can't QUITE get there.
   • Thus, we eventually run out of bits to encode increasingly smaller fractional values.
   • Thus, we have a truncation error.