EECE 320 Midterm, Fall 2009

American University of Beirut Faculty of Engineering and Architecture Electrical and Computer engineering Department EECE 320 Digital Design Midterm Tuesday December 1st, 2009 Name ________________________________________ ID _________________________ Dr. Lama Hamandi Duration: 1h :30 min Question 1 10 Question 2 7 Question 3 10 Question 4 12 Question 5 15 Question 6 10 Question 7 36 Total Grade 100 Instructions:  Check to insure that you have a complete copy of the examination. There are 7 Questions, and a total of 12 pages.  This examination is closed book and closed notes.  The use of Electronic calculators or other equipment is not allowed during the examination.  No use of scratch paper is allowed. You should work your Questions directly on the Question statement sheet in the appropriate space only. You may use the backside of the exam sheets as appropriate.  Include all steps and calculations as appropriate for maximum credit. Be clear, brief, and specific in your answers. Good Luck! Boolean Algebra Theorems X+0=X X.1=X X+1=1 X.0=0 X+X=X X.X=X (X’)’ = X X+X’=1 X.X’=0 X+Y = Y+X XY = YX (X+Y)+Z = X+(Y+Z) = X+Y+Z (XY)Z = X(YZ) = XYZ X(Y+Z)=XY + XZ X + YZ = (X+Y)(X+Z) XY + XY’ = X (X+Y)(X+Y’) = X X + XY = X X(X+Y) = X (X+Y’)Y = XY XY’+Y=X+Y (X+Y+Z)’ = X’.Y’.Z’ (XYZ)’ = X’+Y’+Z’ (X+Y)(X’+Z) = XZ + X’Y XY+X’Z = (X+Z)(X’+Y) XY+YZ+X’Z = XY+X’Z (X+Y)(Y+Z)(X’+Z) = (X+Y)(X’+Z) X 0 = X X  1 = X’ X  X = 0 X  X’ = 1 X  Y = Y  X (X  Y)  Z=X  (Y  Z) =X  Y  Z X (Y  Z) = XY  XZ (X  Y)’ = X  Y’ = X’  Y = XY  X’Y’ EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 2 Question 1: (10 points) A combinational circuit receives a 4-bit BCD number WXYZ and computes the product of WX and YZ. For example if the input is WXYZ = 0111, then the output is 01 * 11 = 1 * 3 = 3. Draw the truth table only of this circuit. EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 3 Question 2: (7 points) Express F as minimum Sum of product: F = (B+AC)(B’+D)(BD+A’) EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 4 Question 3: (10 points) Write F as minimal product of sums. ab cd 00 01 11 10 00 0 1 0 X 01 1 1 1 X 11 0 X X 0 10 X 0 0 0 F1 EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 5 Question 4: (12 points) The following PAL is used to implement a combinational circuit with 4 inputs A, B, C and D. Find the outputs X, Y and Z as minimal sum of products. EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 6 A B C D x x x x x x x x x Y Z x x x x x x X x x x Question 5: (15 points) Minimize this function using a K-map, and draw it using only NAND gates. F(A,B,C,D) = A'B'C' + ABD + A'C + A'CD' + AC'D + AB'C'+A’B’D EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 7 Question 6: (10 points) Write F as a minimal sum of product. EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 8 A’ B’ C D E Question 7: (36 points) 1. A Half adder (HA) is a combinational circuit that adds two bits and generates a Sum bit and a Carry out bit. Draw the truth table of this circuit, and derive minimal algebraic expressions for S and C. (10 points) EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 9 HA A B C S 2. Write the VHDL code to define the entity HA, and write the Dataflow architectural description for this entity. (13 points) EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 10 3. We would like to add the 3 bits of a 3-bit number N2N1N0 using the following circuit. Write the VHDL code to define the entity 3-bit adder, and write the structural architectural description for this entity. (13 points) EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 11 HA A B C S HA A B C S N2 N1 N0 C S EECE 320 Digital Design – Midterm Fall 2009-2010 1-Dec-2009 12