Problem 1 (30 pts) This problem explores the design and use of decoder circuits. Review (redo) zyBook Section 6.4 before starting the problem. (5 pts) Give a simple English description of what a decoder does. What is the mathematical relationship between the number of inputs and the number of outputs? a) b) (5 pts) can you use Karmaugh maps to similify the logic equations resuting from the truth table for a 2x4 decoder? Why or why not? (5 pts) Draw a truth table showing that the following logic gates are equivalent. Which property of Boolean algebra does this illustrate? c) d) (5 pts) Given the insight from Part d, draw a logic diagram for a 2x4 decoder similar to that uses only inverters and NOR gates (5 pts) What is the advantage of replacing AND gates with NOR gates in the design of a decoder? Give enough detail in your answer that we're convinced that we know what you're talking about. Hint: think transistor level design. (5 pts) Describe a real-world application where a decoder circuit would be useful. e) f)