Individual Homework 2 -- EECS 270, Spring '23

Due Monday May 15th @9pm, half credit if turned in by 11pm


This assignment is worth about 1% of your grade in the class and is graded out of 30 points. Remember you may drop one individual homework assignment.

  1. Convert values into the representation given.[2]
    1. 3410 → base 2
    2. 13710 → base 16
    3. 2C216 → base 2
    4. 100010100010010000102 → base 16
  2. Convert values into the representation given, if the value can't be represented say "value out-of-range" [4]
    1. 3210 → 6-bit 2's complement
    2. -3210 → 6-bit 2's complement
    3. -1310 → 4-bit 2's complement
    4. 010 → 5-bit 2's complement
    5. 3810 → 8-bit 2's complement
    6. -16010 → 8-bit 2's complement
    7. -12210 → 8-bit 2's complement
    8. 12210 → 8-bit 2's complement
  3. Consider a 4-bit adder. Indicate what each of the sum and carry bits would be for the following additions. In addition, indicate what the operation being performed would be if the numbers being added were 4-bit 2's complement numbers and also if they were 4-bit unsigned numbers. For example: 0100+1000 would have the sum bits be 1100, the carry bits be 0000, and the operation would be 4+(-8)=-4 as a 2's complement numbers and 4+8=12 as an unsigned numbers. Recall that not all operations will generate a correct answer. Circle those results that are incorrect. You are to assume the 4 sum bits are the result (right or wrong) [3]
    1. 1011+0010
    2. 0010+0011
    3. 0110+1111
  4. Using only a decoder and an OR gate, draw a circuit which implements the following: !(A+B)+!A*C Show your work. [4]
  5. Using gates, design a 4-bit 2's complement greater than comparitor. You really, really want to design a 1-bit comparitor and use those to make the 4-bit one, perhaps with some additional logic. Might want to search the text a bit. [6]
  6. 3.2 [1]
  7. 3.3 [1]
  8. 3.7 [3]
  9. 3.14 (3.15 in 1st) [3]
  10. Consider the following figure. Assume each NOR gate has a delay of 1 time unit. Fill in the timing diagram assuming that the distance between horizontal lines is also 1 time unit (think of it as a nanosecond or whatever). [3].