The following guidelines are expected for all homework submissions:

Problems for Assignment #3

Learning Outcomes: 1) Understanding different number representations; 2) Practice with the different common number bases used by computers; 3) Practice translating values between different bases; 4) Practice translating values between different representations; and 5) Practice/understanding of carry, overflow, saturated, and modular computer arithmetic

Please do all these problems without using a computer or calculator. The purpose of these exercises is to help you develop your skill. Taking the time to practice will give you a better ability and understanding of the material.

Questions about carry and overflow assume signed modular arithmetic, not saturated arithmetic.

These problems give you practice to demonstrate a basic understanding of the concepts of translating between binary and decimal and hexadecimal, along with modular/saturated arithmetic and carry/overflow.

The problems in this section are very straightforward and should not be hard ~ you'll get good practice here!

  1. Hex FAC3 in binary is:
  2. Hex FAC3 as an unsigned decimal is:
  3. Hex FAC3 as a signed decimal is:
  4. Hex 0064 in binary is:
  5. Hex 0064 as an unsigned decimal is:
  6. Hex 0064 as a signed decimal is:
  7. Hex 8000 in binary is:
  8. Hex 8000 as an unsigned decimal is:
  9. Hex 8000 as a signed decimal is:
  10. Decimal 8000 encoded in 16-bits (unsigned) is in hex:
  11. Decimal 8000 encoded in 16-bits (signed) is in hex:
  12. Decimal -11 encoded in 16-bits (signed) is in hex:
  13. Decimal -32717 encoded in 16-bits (signed) is in hex:
  14. Binary 10111101 in hex is:
  15. Binary 1011110100000001 as an unsigned decimal is:
  16. Binary 1011110100000001 as a signed decimal is:
  17. If we had 20-bit registers, the smallest signed decimal integer value would be:
  18. If we had 20-bit registers, the largest signed decimal integer value would be:
  19. The modular sum of 16-bit hex values 3511 + 4FFC is:
  20. The saturated sum of 16-bit hex values 3511 + 4FFC is:
  21. The 16-bit operation 0x3511 + 0x4FFC has a carry (Y or N):
  22. The 16-bit operation 0x3511 + 0x4FFC has a overflows (Y or N):

These problems give you more to think about with the concepts of number conversion and arithmetic.

  1. The modular sum of 16-bit hex values 6159 + F702 is:
  2. The saturated sum of 16-bit hex values 6159 + F702 is:
  3. The 16-bit operation 0x6159 + 0xF702 has a carry (Y or N):
  4. The 16-bit operation 0x6159 + 0xF702 has a overflows (Y or N):
  5. The modular sum of 16-bit hex values EEEE + C00C is:
  6. The saturated sum of 16-bit hex values EEEE + C00C is:
  7. The 16-bit operation 9EEE + AB0C has a carry (Y or N):
  8. The 16-bit operation 9EEE + AB0C has a overflows (Y or N):
  9. The negation of 16-bit word 0xB00F is:
  10. The negation of 16-bit word 0x2232 is:
  11. The negation of 16-bit word 0x8000 is:
  12. The negation of 32-bit word 0xFFF329BA is:
  13. 96.03125 as a 32-bit float, in hex is:
  14. -16777216 as a 32-bit float, in hex is:
  15. Hex 43700000, when interpreted as an IEEE-754 pattern, is in decimal:
  16. Hex C0FF0000, when interpreted as an IEEE-754 pattern, is in decimal:

These problems are difficult and will require you to do some research to get the answers. They are considered optional and you will get extra credit for getting them correct, one point per problem. For any you attempt for which your answer is incorrect, you will NOT be penalized, you just won't get any credit for that one.

  1. The largest finite IEEE-754 single precision float, in hex is:
  2. The smallest finite IEEE-754 single precision float, in hex is:
  3. The largest nonzero negative IEEE-754 single precision float, in hex is:
  4. The smallest nonezero positive IEEE-754 single precision float, in hex is:
  5. -5.125 X 290 as a 32-bit float, in hex is:
  6. 2-138 as a 32-bit float, in hex is:
  7. 1.5 X 2-143 as a 32-bit float, in hex is:
  8. Try this for a challenge, a puzzle, or the experience:
    Hex C059000000000000, when iterpreted as a 64-bit IEEE-754 pattern, is in decimal: