a$.$ An encoder is needed to create a two$-$bit signal to indicate the state. In other words, the truth table for the encoder is below. Design an encoder to create the desired output signal.

$\backslash$table$[[$Off$,$Low,Med,High,Output,$],[1,0,0,0,0,0],[0,1,0,0,0,1],[0,0,1,0,1,0],[0,0,0,1,1,1]]$

b$.$ The two$-$bit signal is sent to another location where a decoder converts the signal to a four bit signal with an LED connected to each bit such that when the bit goes HIGH, the LED for that bit lights and indicates the state of the knob. Design the decoder which will create the four bits from the two bit signal. PLEASE DRAW OUT THE ENCODER AND DECODER.