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7) (Synthesis of a decomposed Boolean function by exploiting don't care conditions - 20 points) Consider the Boolean function F(a, b, c, d, e) whose K-map is shown below in Fig. 2 (i). Now suppose that a logic synthesis algorithm decomposes F as F(a., b, c, d, e)h(go(a, b, e), 91 (a, b, c), d, e), shown in Fig. 2, where the SOP representations are: . Functions go = abc + abe + abd and gl = a,b,c + abc You are asked to solve the following: a) From the K-map of F(a, b,c,d, e), identify a minimum SOP form representation of F in its undecom- b) Now assume the a decomposition is applied as shown in Fig. 2. Minimize the SOP form of go.g1,h c) This decomposition creates don't care conditions at the input of the h(go, 9i,d, e) block. Identify the d) Using the don't care conditions, minimize the SOP form of h. What is the total SOP literal cost of posed form in terms of the primary inputs (a.h.e d,e). What is the SOP literal cost of F Are they already given in minimal form? don't care conditions at the input of h 90,g1 and h. Do the don't care conditions result in further logic simplification with literal cost savings? 7) (Synthesis of a decomposed Boolean function by exploiting don't care conditions - 20 points) Consider the Boolean function F(a, b, c, d, e) whose K-map is shown below in Fig. 2 (i). Now suppose that a logic synthesis algorithm decomposes F as F(a., b, c, d, e)h(go(a, b, e), 91 (a, b, c), d, e), shown in Fig. 2, where the SOP representations are: . Functions go = abc + abe + abd and gl = a,b,c + abc You are asked to solve the following: a) From the K-map of F(a, b,c,d, e), identify a minimum SOP form representation of F in its undecom- b) Now assume the a decomposition is applied as shown in Fig. 2. Minimize the SOP form of go.g1,h c) This decomposition creates don't care conditions at the input of the h(go, 9i,d, e) block. Identify the d) Using the don't care conditions, minimize the SOP form of h. What is the total SOP literal cost of posed form in terms of the primary inputs (a.h.e d,e). What is the SOP literal cost of F Are they already given in minimal form? don't care conditions at the input of h 90,g1 and h. Do the don't care conditions result in further logic simplification with literal cost savings