Computer Architecture

Chapter 6 Problems:

• 1. Rework problem 4 from the chapter 4 homework. Optimize the design and draw the circuit.
• 2. Rework problem 7 from the chapter 4 homework. Optimize the design and draw the circuit.
• 3. Vahid 6.3
• 4. Vahid 6.4
• 5. Vahid 6.5
• 6. Vahid 6.6
• 7. Vahid 6.10 part A
• 8. Vahid 6.11 part A
• 9. Find all the prime implicants for the following Boolean functions and determine what are essential:
  • A. F(W,X,Y,Z) = SUMm(0,1,3,4,6,7,11,13,15)
  • B. F(A,B,C,D) = SUMm(3,5,11,13,14,15)
  • C. F(W,X,Y,Z) = PRODUCTM(2,4,5,6,7,8,10,11,15)
  • D. F(W,X,Y,Z) = PRODUCTM(0,1,4,5,6,11,12,13,15)
• 10. Simplify the following functions using a map:
  • A. F(A,B,C,D) = SUMm(0,4,6,7,9,11,12,13,14,15)
  • B. F(A,B,C,D) = PRODUCTM(2,4,5,6,7,8,10,12,14)
  • C. F(X,Y,Z) = SUMm(1,2,4,7)
  • D. F(X,Y,Z) = PRODUCTM(0,2,3,5,7)
• 11. Simplify the following Boolean expressions using a map:
  • A. WXY'Z' + W'XY' + W'X'Z + X'YZ' + WX'Y
  • B. A'BC' + A'CD + AC'D' + AB'D + ABC
• 12. Simplify the following expressions in sum-of-products and product of sums form:
  • A. C'D + (AD + A'B)C' + (AC + A'B')D
  • B. (A + B + D')' + (A' + B' + C')' + (A'C' + AC)D + A'CD'
  • C. X'Y + XZ + YZ
• 13. Simplify the following functions F together with the don't care conditions d:
  • A. F(A,B,C) = SUMm(0,1,5,6), d(A,B,C) = m(2,4)
  • B. F(A,B,C) = SUMm(0,4), d(A,B,C) = m(3,7)
  • C. F(W,X,Y,Z) = SUMm(4,5,6,9,12), d(WXYZ) = m(0,2,3,7,8,11,15)
• 14. From chapter 4 problem 9 homework the solution took 16 multipliers and 12 adders. Create new designs to solve this problem.
  
  • A. Design a version of the circuit with only one multiplier and one adder.
  • B. Design a pipelined version of the circuit.