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EE2301Dis2F09Sol

# EE2301Dis2F09Sol - Department of Electrical and Computer...

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1 Department of Electrical and Computer Engineering University of Minnesota EE 2301 Fall 2009 Introduction to Digital System Design L. L. Kinney Discussion II Solutions Sept. 17 & 18: Topics are arithmetic with 1 and 2’s complement numbers, Boolean algebra identities, switch networks, canonical expressions and tables of combinations. 1. a) Represent the following decimal numbers as hexadecimal numbers using 15’s (1’s) complements: 45, 83, -45 and -83. b) Using the hexadecimal representations from part a) perform the following operations: 45 + (-83), (-45) + (83), (-45) + (-83). Verify that the sum is correct or else show that overflow occurs. c) Repeat Part a) using 16’s (2’s) complement numbers. d) Repeat Part b) for the 16’s complement numbers. a) 45 10 = 2D 16 , 83 10 = 53 16 , -45 10 = D2 16 , -83 10 = AC 16 b) 2D 16 + AC 16 = D9 16 = (-38 10 ), D2 16 + 53 16 = 26 16 = (38 10 ), D2 16 + AC 16 = 7F 16 = (127 10 ) = (-128 10 ) overflow c) 45 10 = 2D 16 , 83 10 = 53 16 , -45 10 = D3 16 , -83 10 = AD 16 d) 2D 16 + AD 16 = DA 16 = (-38 10 ), D3 16 + 53 16 = 26 16 = (38 10 ), D3 16 + AD 16 = 80 16 = (-128 10 ) 2. Prove the following theorems of Boolean algebra and identify the identities of Boolean

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