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Main points of this past exam are: Most Positive, Numbers of Reason, Computer Engineering, Decimal Notation, Hexadecimal Notation, Binary Notation, Convert the Following Notations, Expressed in Decimal, Signed Representations, Floating Point Representation
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4 problems, 5 pages Exam Two 9 March 2011
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
31 24 24 21 100
4 problems, 5 pages Exam Two 9 March 2011 Problem 1 ( 3 parts, 31 points) Numbers of Reason Part A ( 13 points) Convert the following notations:
binary notation decimal notation 1 1100 1001. 1001 497
binary notation hexadecimal notation 101 1010 0101.0101 1010 101 CA11.CAB
Part B (12 points) For the 25 bit representations below, determine the most positive value and the step size (difference between sequential values). All answers should be expressed in decimal notation. Fractions (e.g., 3/16ths) may be used. Signed representations are two’s complement.
representation most positive value step size unsigned fixed-point ( 20 bits). ( 5 bits) signed integer ( 25 bits). (0 bits) signed fixed-point ( 13 bits). ( 12 bits) signed fixed-point ( 9 bits). ( 16 bits)
Part C ( 6 points) A 25 bit floating point representation has a 17 bit mantissa field, a 7 bit exponent field, and one sign bit.
4 problems, 5 pages Exam Two 9 March 2011 Problem 3 (3 parts, 24 points) Achieve a Happy State Part A ( 10 points) Implement a transparent latch using only pass gates and inverters.
Part B ( 8 points) Implement a one bit register with write enable using only the components drawn below. Label inputs In , write enable WE , clocks ф 1 , and ф 2 , and output Out.
In Out En
Latch
In Out En
Latch
I
I1S
2to1mux
Part C (6 points) Assume the following signals are applied to a register. Draw the output signal Out. Draw a vertical line where In is sampled. Draw crosshatch where Out is unknown.
4 problems, 5 pages Exam Two 9 March 2011 Problem 4 (3 parts, 21 points) “A chip off the old block” Part A ( 15 points) Consider the five definitions for the block drawn below. One block input is the logical value A. The other input is the control value C. The output behavior for each of the five definitions is given in the table. Complete the full truth table and state the logical (gate) names for each definition. (hint: the first block one appears to mask A when its control input is low.)
A IN C
A 0 0 A A A Zo A 1 A A 0 1 A
Part B ( 6 points) The circuit below is built using these blocks. Describe its behavior. Also give the circuits common name.
X
Y
C O
I (^) N C
I (^) N O C
O
I N C
O (^) IN^ C O
X Y Out 0 0 1 0 0 1 1 1
It's a
