Answer the following :-

1. Simplify the following Boolean expressions using four variable karnaugh map to sum of products also find product of sums: a. F(a,b,c,d)= (0,1,2,3,4,6,8,9,12,14) b. F(a,b,c,d)=TI (2,4,6,8,9,11,10) 2. Simplify the Boolean function; together with don't care conditions d. c. F(a,b,c,d)= (0,1,2,3,10,12,13,14,15) d(a,b,c,d)= E(6,7,8,11) d. F(a,b,c)= II (0,1,3,5) d(a,b,c)= II (4,7) 3. Design a circuit for Full Adder using two half Adders and OR Gate? 4. Design and explain a 3-bit Binary Adder with block diagram and circuit diagram? 5. Design and explain a 3-bit Binary Subtractor with block diagram and circuit diagram? 6. Design and explain a 3-bit Binary Adder-Subtractor with block diagram and circuit diagram? 7. Design a 3X8 Decoder using NAND Gates? 8. Design a 2-to-4 line Decoder using AND Gates