Could you please help explain what S{2, 3, 4}(x1,x2,x3,x4,x5,x6) represent? Thank you very much.

 

ECE462:LOGIC SYNTHESISDepartment of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignJ. H. PatelFall 2016PROBLEM SET No. 4Issued: Thursday September 15, 2016Due: Tuesday September 20, 2016Objective of this mini-homework is to understand Symmetric Functions, Threshold Functions, and LogicHazards.1.Symmetric Functions: Fill in the answersa.S{2, 3, 4}(x1,x2,x3,x4,x5,x6) + S{1,3,5}(x1,x2,x3,x4,x5,x6) = S{…?….}(x1,x2,x3,x4,x5,x6)b.S{2, 3, 4}(x1,x2,x3,x4,x5,x6)S{1,3,5}(x1,x2,x3,x4,x5,x6) = S{…?….}(x1,x2,x3,x4,x5,x6)c.S{2, 3, 4}(x1,x2,x3,x4,x5,x6)⊕S{1,3,5}(x1,x2,x3,x4,x5,x6) = S{…?….}(x1,x2,x3,x4,x5,x6)d.S{1, 3, 4}(x1’,x2’,x3’,x4’,x5’,x6’) = S{…?….}(x1,x2,x3,x4,x5,x6)e.S{2, 3, 4}(x1’,x2’,x3’,x4’,x5’,x6’) = S{…?….}(x1,x2,x3,x4,x5,x6)2.Threshold Functions: Give the set of inequalities for the weights of functionF(x1,x2,x3) = x1x2+ x1x3Compute the weights and threshold using only integers.3.Transient Analysis: In the class we discussed AND function of steady 0 and 1, rising and fallingsignals. Give a similar table for (a) NAND and (b) OR function assuming similar worst casebehavior.AND0 100 0 0010 1004.Logic Simulation of Transients: For the following XOR circuit, with inputs A and B, simulate thetransient propagation as discussed in the class, for B= steady 1 and A =Repeat the same analysis with logic simulation of three input vectors AB = 01, U1, 11Comparethese two simulations giving your own insights on the effort, accuracy etc.ABDEJCYHLKGF1