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.

C-level Problems

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 problem set is PASS/FAIL meaning if you miss one problem you get a zero for the assignment. However, don't fret, you'll have an extra week to do it again and re-submit for full credit. No lateness penalties for re-submits unless you miss the deadline.

  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):

B-level Problems

These problems give you more to think about with these concepts of number conversion and arithmetic. The problem set is PASS/FAIL meaning if you miss one problem you get a zero for the assignment. However, don't fret, you'll have an extra week to do it again and re-submit for full credit. No lateness penalties for re-submits unless you miss the deadline.

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

A-level Problems

These problems are difficult and will require you to do some research to get the answers. The problem set is PASS/FAIL meaning if you miss one problem you get a zero for the assignment. However, don't fret, you'll have an extra week to do it again and re-submit for full credit. No lateness penalties for re-submits unless you miss the deadline.

  1. Complete all the C-level AND B-level problems plus the following:
  2. The largest finite IEEE-754 single precision float, in hex is:
  3. The smallest finite IEEE-754 single precision float, in hex is:
  4. The largest nonzero negative IEEE-754 single precision float, in hex is:
  5. The smallest nonezero positive IEEE-754 single precision float, in hex is:
  6. -5.125 X 290 as a 32-bit float, in hex is:
  7. 2-138 as a 32-bit float, in hex is:
  8. 1.5 X 2-143 as a 32-bit float, in hex is:
  9. OPTIONAL — Try this for a challenge, a puzzle, or the experience:
    Hex C059000000000000, when iterpreted as an IEEE-754 pattern, is in decimal: