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EE2301EX1F08Sol - University of Minnesota Department of...

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University of Minnesota Department of Electrical and Computer Engineering EE2301 Fall 2008 Introduction to Digital System Design L. L. Kinney Exam I (Closed Book) Solutions 1(12) What range of numbers can be represented by the following number systems? (a) 8-bit binary, unsigned (positive) numbers. (b) 8-bit binary, one’s complement numbers. (c) 8-bit binary, two’s complement numbers. (d) 2-digit hexadecimal, 15’s complement numbers. Solution (a) 0 to +255. (b) -127 to +127 (c) -128 to +127 (d) -127 to +127 2(10) A weighted code with weights 7, 3, 1 and -2 is used to represent the hours of the day 0 to 11. Construct a table showing the representation of the hours with this code. If more than one codeword can be used for an hour, choose the codeword containing the fewest 1’s. Solution h 7 3 1 -2 0 0 0 0 0 1 0 0 1 0 2 0 1 1 1 3 0 1 0 0 4 0 1 1 0 5 1 0 0 1 6 1 0 1 1 7 1 0 0 0 8 1 0 1 0 9 1 1 1 1 10 1 1 0 0 11 1 1 1 0 Unused 7 3 1 -2 -2 0 0 0 1 -1 0 0 1 1 1 0 1 0 1 8 1 1 0 1
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2 3(25) A switching function f(A, B, C, D) has don’t cares d(2, 5, 8, 11, 14). One switching
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