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ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm I am providing this list of sample problems and their solutions to give you an idea of the type of problems you COULD encounter on the mid-term. Please note that anything that we have covered in class during the first half of the semester can show up on your mid-term. Typically I will give you 4-5 problems. I will also provide a list of the Basic Boolean Identities. 1/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm Problem #1: (25 points) Binary Codes and Number Systems a) (5 points) How many bits do you need to have a binary code for 286 items? 28= 256 29=512 THEREFORE 9 bits are needed a) (5 points) Represent the fixed point base 10 number (82.25) 10 in base 2. 1010010.01 a) (5 points) Represent the base 10 number (82.25)10 using binary coded decimal (10000010.00100101)BCD a) (5 points) Represent the base 2 number (101001001001001111001)2 in hexadecimal (149279)16 a) (5 points) What is 0xAF230 in binary? (1010 1111 0010 0011 0000)2 2/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm Problem 2: (25 points) Boolean Algebra a) (15 points) Derive the simplified SOP of the following expression using Boolean algebra. Please show your work to receive full credit. F = x1 x 2 x 3 + x1 x 2 x 3 + x1 x 3 x 4 + x 4 x1 + x1 x1 = x1 x 2 x 3 + x1 x 2 x 3 + x1 x 3 x 4 + x 4 x1 + 0 = x1 x 2 (x 3 + x 3 ) + x1 x 3 x 4 + x 4 x1 = x1 x 2 + x1 (x 3 x 4 + x 4 ) = x1 x 2 + x1 (x 3 + x 4 ) = x1 x 2 + x1 x 3 + x1 x 4 a) (10 points) Apply DeMorgan’s Theorem to the following expression to simplify into SOP form. † F = x1 x 2 x 3 x 4 + x 5 = (x1 x 2 x 3 x 4 )x 5 = (x1 x 2 x 3 + x 4 )x 5 = ((x1 + x 2 )x 3 + x 4 ) x 5 = x1 x 3 x 5 + x 2 x 3 x 5 + x 4 x 5 † 3/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm Problem #3: (25 points) CMOS circuit Design a) (10 points) Design the complex CMOS circuit to implement the following function. Assume that you have the complemented and un-complemented version of the input variables at your disposal. BE SURE YOU LABEL THE OUTPUT OF CIRCUIT. F = x1 x 2 + x 3 † Vdd Logic “1” X1 X2 X3 F X1 X3 X2 GRD Logic “0” 4/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm b) (10 points) Given the following nFET network, please draw the corresponding pFET network. Once completed, draw a line through network to show the conducting path through this network for x1 = LOW, x2=LOW, x3=HIGH, x4=LOW. Is the output high or low? Vdd X1 X2 X3 X4 x1 x3 x2 x4 GRD b) (5 points) What does the acronym MOSFET stand for? Metal Oxide Semiconductor Field Effect Transistor 5/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm Problem 4: (25points) Gate Design Methodology (a) (10 points) Consider the following schematic that is provided with no information other than that the designer used mixed logic notation. Write down the original Boolean function that the designer used to make this logic schematic. F = X + Y + Z + ABC Y † X Z A B F C (b) (10 points) Implement the following function using OR gates only. Be sure you use mixed logic notation. Assume that you only have the un-complemented form of the signals available to you. BE SURE THAT YOU DO NOT TRY TO ALTER F WITH BOOLEAN ALGEBRA. After you finish your circuit be sure you indicate how many transistors you need. F = x1 x 2 + x 3 # Transistors = 20 2 6 X1 † 6 2 X2 2 X3 2 6/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm c) (5 points) Show the most efficient transistor level CMOS circuit implementation of an OR function. Assume that you have available to you the un-complemented signals X and Y (i.e. if you need the complement you must show that) 4 2 NOR GATE Vdd Inverter X Vdd Y X+Y X Y GRD GRD 7/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm Problem #5 (20points) –Building Blocks Fill in the truth table that describes the output of the following circuit. Z 4-to-1 MUX 0 1 2 output 3 + S1 S0 Vdd - GRD Y X Y X Z output 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 8/9 ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample Midterm Problem #6 (20points) – Number Systems (a) (5 points) The following number is a 5-bit signed number that uses 2’s complement to represent negative numbers. Give the decimal equivalent. (10010)2 = (?)10 1) We know it is negative because MSB is 1 2) To get the positive magnitude take the 2’s complement (i.e. flip the bits and add 1) 01101 + 1 -14 01110 -----> 14 (b) (5 points) Using the same 5-bits in part (a) NOW assume that the number is a signed number that uses signed-magnitude representation of negative numbers. Give the decimal equivalent. (10010)2= (?)10 1) We know that it is negative because the MSB is 1 2) With signed magnitude, we can read the other bits as a postive number 0010 ---- > 2 -2 9/9

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posted: | 11/21/2008 |

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