Home Assignment No-3 Subject: Course: Instructor:
Digital Logic Design BIT-11 Arshad Nazir
Marks: Issue: Due on:
100 08 Nov 2010 15 Nov 2010 (09:00 AM)
Note:
Attempt the given problem set in a sequential order. Be neat and show complete work. Make an index on the first page showing summary of the problems solved along-with page numbers and also specify the missing ones. No late submissions will be accepted unless prior approval from the teacher has been obtained under extreme exigencies. The assignments submitted after due date/time will be graded zero . Plagiarism is the unacknowledged use of other people’s work, including the copying of assignments from the other students. Plagiarism is considered as a serious offence by the university and serious penalties apply. Any assignment found copied will be graded zero and strict disciplinary action will also be initiated against the students involved in cheating. All the students will submit a certificate with the assignment work stating the originality of their efforts with no copying from others. Note that Twenty Marks are reserved for presentation, quality work, table of contents, and certificate attached with the assignment work.
Problem No-1
Optimize the following Boolean functions together with the don’t care conditions d in sum-of-products form using map method by finding all the prime implicants and essential prime implicants and applying the selection rule: a. f(a,b,c,d)= ∑m (2,4,5,6,9,10,11,12,13,15) b. F1 (A,B,C,D)=(A +B +B + D )(A+B )(A+B +C +C )(A )(A + B+D )(B+C )(B+C +D +D ) c. F2(W,X,Y,Z)= ∑m (0,1,5,5,8,9,11,13,)+ ∑d (7,10,12)
Problem No-2
Four large tanks at a chemical plant contain different liquids being heated. Liquid-level sensors are being used to detect whenever the level in tank A or tank B rises above a predetermined level. Temperature sensors in C and D detect when the temperature in either of the tanks drops below a prescribed temperature limit. Assume that the liquid-level sensor outputs A and B are LOW when the level is satisfactory and HIGH when the level is too high. Also, the temperature sensor outputs C and D are LOW when the temperature is satisfactory and HIGH when the temperature is too LOW.
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Design a logic circuit that will detect whenever, the level in tank A or tank B is too high at the same time that the temperature in either tank C or tank D is too low. Implement the design using two-level (a) NAND-AND, (b) AND-NOR, (c) OR-NAND, and (d) NOR-OR forms. Problem No-3
Find a minimum sum-of-products expression for the following function together with the don’t care conditions d using map method. Underline the essential prime implicants in this expression. f(v,w,x,y,z)= ∑m(0,2,6,7,8,10,11,12,13,14,16,18,19,29,30) d(v,w,x,y,z)= ∑d(4,9,21)
Problem No-4
Obtain the minimum sum-of-products expression for the following function using G(A,B,C,D,E,F)= (1,3,6,8,9,13,14,17,19,24,25,29,32,33,34, 35,38,40,46,49,51,53,55,56,61,63) a. Map method b. Quine-McCluskey(Tabulation)method
Problem No-5
Implement the given two-level function using f(x1,x2,x3,x4,x5,x6,x7)=x1x4x5+x1x4x6+x1x7+ x2x3x4x5+ x2x3x4x6+x2x3x7) a. Multi-level NAND gates b. Multi-level NOR gates only Assume that NAND and NOR gates have a fan-in of three and two respectively and the input variables are available in un-complemented form only.
Derive the circuits for a four-bit parity generator and five-bit parity checker using odd parity. _______________________________________________________________ “Good Luck” Problem No-6
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