Q.1. Using algebraic manipulation, simplify the following expressions to minimum number of literals and express the simplified function as SOP (sum of products i.e. AND terms that are ORed) and POS (product of sums i.e. OR terms that are ANDed): (1) F(A,B,C) = A'B'C' + A'BC + A'B'C + ABC (1) F(A,B,C) = (A+B+C) (A'+B'+C') (A+B'+C') (A+B+C') (ii) F(A,B,C,D) =A'B'D + A'D + BC (A' + D') (should be simplified to 5 literals only) (iii) F(A,B,C,D) = (A+B+C+D') (A+B+C'+D') (A+B'+C+D') (A+B'+C'+D') Hint: Ta

3. The function of 3 variables is specified as a sum of minterms: F (A, B, C) = (0, 1, 3, 4, 5). 3a) Specify the function F as a product of Maxterms. 3b) Specify the complement to the function as a sum of minterms (for F'). 3c) Obtain the schematics for the following implementations of function F: 3c1) with a 3-to-8 decoder with active-high outputs and a single 3-input logic gate. 3c2) with a 3-to-8 decoder with active-low outputs and a single 3-input logic gate. The available gates are OR3, NOR3, AND3, and NAND3. Denote the decoder inputs with A2 (for MSB), A1, AO (for LSB). Assign the variables A, B, C to the decoder inputs. The decoder outputs should be denoted with decimal digits from 0 to 7 which represent minterm or Maxterm numbers in accordance with the decoder output type.

5. Simplify the following functions using a K-map: g)F(X,Y,Z)=XY'Z+X'+Z+Y'Z'

1. Reduce the following function: ((A O B)•(A•C) )•( (A•B) +(A © B) )