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Computer Organization and Architecture

   

Added on  2021-04-16

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COMPUTER ORGANIZATION AND ARCHITECTUREAssignment 1: Data Representation and Digital LogicName of the Student:Student ID:Subject Code:ITC544Page 1 of 8

COMPUTER ORGANIZATION AND ARCHITECTUREQuestion 1a. Determine the value of base x if (152)x= (6A)16Solution: Given,(152) x= (6A) 16LHS,(152) x= X2 + (5 * X1) + (2 * X0)= X2 + 5X + 2RHS,(6A) 16= (6 * 161) + (10 * 160)= 106Since, LHS=RHS. Therefore, X2 + 5X + 2=106=) X2 + 5X - 104 = 0=) X2 + 13X - 8X – 104 = 0=) X(X + 13) – 8(X + 13) = 0=) (X - 8) (X + 13) = 0Therefore, Either X=8 or -13Since, X is a base and hence it cannot be in negative power. Therefore the final solution for X is8. Answer: The value of X is 8 for (152)x= (6A)16b) Convert the followings:i. BED16 into 3-base representationPage 2 of 8

COMPUTER ORGANIZATION AND ARCHITECTUREFor converting BED16 into base 3, first we need to convert it into decimal form, BED16= (B * 162) + (E * 161) + (D * 160)= 2816 + 224 + 13= (3053)10Now, 305310=DivisorDividendRemainder3305323101703339031132337131203411Therefore, (BED)16 = (11012002)3ii) 3217 conversion to base-2For converting 3217 into base 2, first we need to convert it into decimal form, (321)7= (3 * 72) + (2 * 71) + (1 * 70)= (162)10Now, (162)10=DivisorDividendRemainder2162028112400220021002512201Therefore, (321)7= (10100010)2Page 3 of 8

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