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Total marks: 100 Task 1/25 marks Prove the following equations using Boolean algebra identities 1 AC + BC + AB-ACBC AB 2. ABC.AC-ABC+AC Simplify the following expressions to their shortest form 3. AB BC BC + ABC 4. ABC ABC ABC 5. AAB)BAB) Show each step of your operations, name the identities you are using Task 2 125 marks Identify and analyze the original Boolean expression implemented by the circuit shown IF - Express in terms of input variables A,B,C 2. Simplify the original Boolean expression using Boolean algebra identities 3. Show a truth table for the acquired function 4. Draw a new circuit diagram for the acquired function. Do not forget to label input/output, similar to the way they are labeled in the picture above Task 3 125 marks NAND and NOR gates are sometimes referred to as universal gates meaning that with many copies of them, they can be used in various configurations to implement any other logic gates and the Boolean functions they represent) Your task is as follows 1. Show that AND, OR NOT wates can be implemented with only NAND gates Provide a circuit diaram similar to that of Task 2) for each of implemented wates 2. Show that AND, OR NOT wates can be implemented with only NORates Provide a circuit diagram similar to that of Task 2) for each of implemented as 3. Use only NAND wates to implement the following function(show circuit truth table) F, ADAC BC 4. Use only NOR yates to implement the following function (show circuit truth table) F-BDCD+A