Hi, i'm trying to figure out how to do this worksheet and was wondering if anyone could help me out? it would be greatly appreciated. This worksheet is based on Boolean algebra and adders. thank you so much.

1. [20pts] Logical completeness Show that you can use only two-input NAND gates to implement each of the following two- input logic finctions and draw the used NAND gates and wiring. a. i. NOR function ii. XOR function b. Show that you can use only two-input NOR gates to implement each of the following two- input logic finctions and draw the used NOR gates and wiring i. NAND function ii. XOR function [10pts] A 2-1 Mux takes two inputs and uses a 1-bit selector value to select one of the inputs for the output. A 1-2 Demux does the opposite taking a single input and using a 1-bit selector to select which one of the two output lines will have the input value while the other output line has a 0 value. Dravw the logic gates and wiring for a 1-2 Demux 2. 3. [10pts] Demonstrate by means of truth tables the validity of the following identities b. A B C (A B) (A + C) 4. [20pts] Prove the identity of each of the following Boolean equations, using algebraic manipulation: 5. [20pts] For the Boolean function O1 and O2, as given in the following truth table Input Output z Ol O2 0 1 11 0 a. List the minterms for a three-variable function with variables x, y, and z. b. Express O1 and O2 in sum-of-product algebraic form. [20pts] In class, we learned the implementation for a 4-bit carry lookahead adder. We can use the same idea and extend to build a 16-bit carry level carry lookahead adder In the textbook, Figure 8.6.3 shows a two-level implementation of a 16-bit carry lookahead adder This adder uses 4-bit carry lookahead adders at the lower level and uses a carry lookahead unit at the higher level. Compare these two implementations and provide your explanation why the two-level implementation could be preferred. 6. lookahead adder. Denote this implementation as a one