Digital design ...kindly solve number 1 up to 6 for me so as to understand key concepts

1. ( 6 points) Simplify the following Boolean expressioas to a miaimum number of literal a) (A+C)(AD+AD)+AC+C b) ABC+ABC+ABC+ABC c) (AB)(A+B)(B+B) 2. (5 poists) Fiad the conplemeat of the following expressioas: a) F1(a+c)(a2+b)(a+b+c) b) F2=(A+C)(BC)+(ABC+AC) 3. (2+2+2+2+2) For the following tndath ble 3. (2+2+2+2+2) For the following truth table a. Show the minterms in numerical form b. Show an algebraic expression of the minterm. c. Simplify the SOP expression d. Show the maxterm in numerical form e. Show the algebraic expression of maxterm. 4. ( 5 points) Convert each of the following to the other canonical form: (a) F(x,y,z)=m(1,3,5,7) (b) F (A, B, C, D) =IM(3,5,8,11,13,15) 5. (5 points) Convert the following Boolean function as standard SOP (numerical form) G(x,y,z)=xy+z+yz a. Convert the following Boolean function as standard POS (numerical form) G(x,y,z)=(x+y)(x+z)(y+z) 6. For the Boolean function F=XYYZ+XYZ+WXY+WXY+WXY a. (9 points) Obtain the truth table of F. b. (5 points) Use Boolean algebra to simplify the function to a minimum number of literals. c. ( 5 points) Compare the simplified function against the un-simplified simplified one and discuss the savings of hardware in terms of no. of gates and no. of inputs