Question:

Please convert the below content to rendered equations without any errors.Got it ? Let’s solve **each part step by step** and clearly arrive at the **simplified Boolean function**. --- ## **Given Question (from image)** **17. Simplify the function (F) together with the don’t care conditions and express the simplified function as:** * **(i) Sum of Products (SOP)** * **(ii) Sum of Minterms** --- ## **(a)** [ F(x,y,z)=\Sigma(0,1,4,5,6), \quad d(x,y,z)=\Sigma(2,3,7) ] ### **Step 1: Observe** * Total minterms for 3 variables = 8 → **0 to 7** * Given minterms + don’t cares cover **all minterms** ### **Step 2: Use don’t cares** Since all remaining minterms are don’t cares, we can group everything in the K-map. ### **Step 3: Simplification** Entire K-map becomes **1** [ \boxed{F = 1} ] ### **Final Answers** * **SOP:** (F = 1) * **Sum of minterms:** (\Sigma(0,1,2,3,4,5,6,7)) --- ## **(b)** [ F(A,B,C,D)=\Sigma(0,6,8,13,14), \quad d(A,B,C,D)=\Sigma(2,4,10) ] ### **Step 1: Plot on 4-variable K-map** * Use **1’s** for minterms * Use **X’s** for don’t cares ### **Step 2: Make largest possible groups** Using don’t cares, optimal groupings give: * Group 1 → (B'D') * Group 2 → (A'C) ### **Step 3: Write simplified function** [ \boxed{F = B'D' + A'C} ] ### **Step 4: Write as sum of minterms** Expand expression: * (B'D') → minterms: 0,2,8,10 * (A'C) → minterms: 6,14 [ \boxed{F = \Sigma(0,2,6,8,10,14)} ] --- ## **(c)** [ F(A,B,C,D)=\Sigma(5,6,7,12,14), \quad d(A,B,C,D)=\Sigma(3,9,11,15) ] ### **Step 1: K-map placement** * Mark **1’s** and **X’s** ### **Step 2: Grouping** Best groupings (using don’t cares): * Group 1 → (CD) * Group 2 → (BC) ### **Step 3: Simplified SOP** [ \boxed{F = CD + BC} ] ### **Step 4: Sum of minterms** * (CD) → 3,7,11,15 * (BC) → 6,7,14,15 Unique minterms: [ \boxed{F = \Sigma(3,6,7,11,14,15)} ] --- ## ✅ **Final Summary** | Part | Simplified SOP | Sum of Minterms | | ---- | -------------- | ------------------------ | | (a) | (1) | (\Sigma(0–7)) | | (b) | (B'D' + A'C) | (\Sigma(0,2,6,8,10,14)) | | (c) | (CD + BC) | (\Sigma(3,6,7,11,14,15)) | --- If you want, I can **draw the K-maps step-by-step** or **verify using Boolean algebra** too ?