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Main points of this exam paper are: Subtraction, Arithmetic, Bit Numbers, Support Subtraction, Consider Error, Digital Logic, Error Occurred, Function That Determines, Most Significant, Being Processed
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4 problems, 5 pages Exam Two 18 October 2000
Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate the pages of the exam. For maximum credit, show your work. Good Luck!
Your Name ( please print ) ________________________________________________
1 2 3 4 total
4 problems, 5 pages Exam Two 18 October 2000
Problem 1 (2 parts, 22 points) Arithmetic
Part A (10 points) The adder below adds two four bit numbers A and B and produces a four bit result S. Add extra digital logic to support subtraction as well as addition. Label inputs X 3 , X 2 ,
X 1 , X 0 , Y 3 , Y 2 , Y 1 , Y 0 , ADD / SUB and outputs Z 3 , Z 2 , Z 1 , Z 0. Do not consider error determination here.
Part B (12 points) Consider a function that determines whether an error occurred when adding or subtracting two two’s complement numbers. Suppose XMSB and YMSB are the most significant bits of the two numbers being processed and ZMSB is the most significant bit of the result. Complete the truth table below to indicate an error (Err) when one has occurred.
Addition (X+Y=Z) Subtraction (X-Y=Z) XMSB YMSB ZMSB Err XMSB YMSB ZMSB Err 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1
4 problems, 5 pages Exam Two 18 October 2000
Problem 3 (2 parts, 20 points) Building Blocks
Consider a priority encoder with the following behavior:
In3 In2 In 1
In 0 O 1 O 0 Valid
Part A (10 points) List the inputs (In 0 , In 1 , In 2 , and In 3 ) in increasing priority.
lowest priority 3 rd^ highest priority 2 nd^ highest priority highest priority
Part B (10 points) Complete the truth table for the following unusual logic block
A B
Out
A B Out
0 0
1 0
0 1
1 1
4 problems, 5 pages Exam Two 18 October 2000
Problem 4 (3 parts, 30 points) Numbers and Karnaugh Maps
Part A (12 points) For the following behavior (in map format), derive a simplified products of sums expression using a Karnaugh Map. Circle and list the prime implicants, indicating which are essential. Then write the simplified POS expression.
simplified POS expression
Part B (9 points) Convert some binary values (and powers of two) into decimal notation:
binary notation decimal notation
111101010
225
Part C (9 points) Convert the following octal values into hexadecimal notation:
octal notation hexadecimal notation
100
450
