Lancaster University CollegeEXAMINATIONS 2018at Beijing Jiaotong UniversityPARTI(First Year)ELECTRONIC AND COMMUNICATIONS ENGINEERINGFundamentals of Digital Electronics(CNENGR116)Example examination paperTime:2 hoursTotal marks available:50Weight:60%Instructions:1.Answer all questions in Section A and answer ONE question from Section B.2.Marks are indicated on right hand side in the parenthesis at the end of the question.3.Please leave all material including question paper in exam hall.Material Required:1.An examination answer book.2.A scientific calculator.Section A:(25 marks)Answer ALL questions(1)Convert the following numbers as per their given radix.(4 marks)(a)(10101)2(b)(11101.11012(c)(127)10(d)(651.475)10(2)Perform the following Binary arithmetic without the use of a calculator.Write down theanswer in binary and show the calculation performed.(2 marks)011011+10011111110-10011(3)Prove the equality of the following Boolean expressions:(4 marks)AB +BCD+ABC +CD=B+CDWY+WYZ+WXZ+WXY =WY+WXZ +XYZ+XYZ(4)Write down the period and duty cycle for the square waveform shown in Figure 1.(1 mark)Time(s)06111524Figure 1(5)Minimise the following expression using a Karnaugh-map and implement using NANDgates only:(5 marks)ABCD +ABCD ABCD ABCD ABCDABCD(6)Explain the half-adder with a gate-level circuit diagram and truth table.(3 marks)(7)Construct a timing diagram for the synchronous counter in Figure 2 showing thewaveforms expected on Qo,Q and Q2.(3 marks)HIGHFF1FF2Figure 2PLEASE TURN OVER2