"Assignment 1: Data representation & Digital logicValue: 15%1. Using a "word" of 5 bits, list all of the possible signed binary numbers and their decimal equivalents that are represent able in:[3 Marks]a. Signed magnitudeb. One's complementc. Two's complementAns. :BINARY DECIMAL SIGNED 1’S COMPLEMENT 2’S COMPLEMENTMAGNITUDE00000 0 0 0 000001 1 1 1 100010 2 2 2 200011 3 3 3 300100 4 4 4 400101 5 5 5 500110 6 6 6 600111 7 7 7 701000 8 8 8 801001 9 9 9 901010 10 10 10 1001011 11 11 11 1101100 12 12 12 1201101 13 13 13 1301110 14 14 14 1401111 15 15 15 1510000 16 -0 -15 -1610001 17 -1 -14 -1510010 18 -2 -13 -1410011 19 -3 -12 -1310100 20 -4 -11 -1210101 21 -5 -10 -1110110 22 -6 -9 -1010111 23 -7 -8 -911000 24 -8 -7 -811001 25 -9 -6 -711010 26 -10 -5 -611011 27 -11 -4 -511100 28 -12 -3 -411101 29 -13 -2 -311110 30 -14 -1 -211111 31 -15 -0 -1 2. A Computer uses IEEE-754 format to represent floating points. What value (in decimal) the computer represents if the floatingpoint is represented using the following binary digits: [3 Marks]1 10000011 11000000000000000000000Ans. : 1 10000011 1100000000000000000000010000011=(131)10 Subtract 127 from 131= 131-127=4 4 -(1. 11000000000000000000000 ) x 22 4 -4 -(11100.0000000000000000000)2 x 2 x 2=-(11100.0000000000000000000) = (-28.0) 103. Using Boolean algebra, prove that: [2 marks]X’Y + XYZ’ + Y’ + XZ (Y+Y’) = 1Ans.L.H.S. : X’Y + XYZ’ + Y’ + XZ(Y+Y’)= X’Y + XYZ’ + Y’ + XYZ + XY’Z= X’Y + XY(Z’ + Z) + Y’ + XY’Z = X’Y + XY + Y’ + XY’Z= Y (X’ + X) + Y’(1 + XZ)= Y + Y’= 1 which is equal to R.H.S. hence proved. 4. Charles Sturt University (CSU) has opened an IT Doctorate study in Sydney Study Centre. The applicant shouldhas a master degree in IT or a master degree in electrical engineering. The applicant should also has completedproject subject (e.g. ITC570, ITC571, …) in his master degree. Before CSU management staff approve student’sapplication, they have to check student master degree if it meet the requirements and also check if the studentcompleted project subject or not in his master degree. After checking applicant documents, CSU staff has come tothe following conclusions:· Approve if applicant has one of the required master degrees and has completed project subject.· Approve if applicant has two of the required master degrees and has completed project subject.· Don't approve otherwise. Construct a truth table and find the minimized Boolean function to implement the logic telling the CSU staff whento approve. Draw a circuit diagram for the Boolean function.[4 Marks = 1+1+2]Ans.Truth table : MASTER DEGREE MASTER DEGREE IN COMPLETED APPROVE ORIN IT ELECTRICAL ENGG. PROJECT DISAPPROVEX Y Z0 0 0 00 0 1 00 1 0 00 1 1 11 0 0 01 0 1 11 1 0 01 1 1 1Minimized Boolean expression :X ’YZ + XY ’Z + XYZCircuit Diagram For The Boolean Expression :5. Complete the truth table for the following sequential circuit: [3 marks]A B X A B0 0 0 1 10 0 1 1 00 1 0 1 10 1 1 0 01 0 0 0 11 0 1 0 01 1 0 1 11 1 1 1 0 RationaleThis assessment task covers topic 2 and 3, and has been designed to ensure that you are engaging with the subjectcontent on a regular basis. More specifically it seeks to assess your ability to:? be able to apply Boolean algebra and digital logic to design and interpret digital circuits.? be able to use different identities of the Boolean algebraMarking criteria Credit (65% - 74%) |Questions Fail (<50%) Pass (50% - 64%) High Distinction (>84%)Distinction (75% - 84%)Neither the The answer is not The answer is correct or thereQuestion 1 Answer is correctanswers are correct correct, but the steps are were only a few slip of pen, or a& 2 All steps were shown.nor the steps. correct. step or two were missing.The circuit design and theThe circuit design Boolean expression is The circuit design is correct. TheBoolean expression are correctis incorrect and not correct, however the Boolean expression is minimised.Question 3 but not minimised. Steps aredoes not conform steps are correct. No or All steps are explained. The circuitcorrect. Minor mistakes in theto the question. wrong circuit diagram. diagram is correct and neat.Boolean algebra.Neither the Answers are all correct but there Answer s are all correct andQuestion 4 Answer is not correct,answers nor the are only few mistakes in the complete. All steps are shown and& 5 but the steps are correct.steps are correct steps. identities are listed "