A decoder is a combinational circuit that is used to select one from among many different possible outputs. For example, if there are several memory chips in a computer, a decoder can be used to select a particular one to use by putting a 1 on that chip's enable line. Decoders have inputs lines onto which a pattern of is and os is put to select one of the output lines, of which there are usually more than there are inputs. Answer the following questions about decoders. Although you could look up decoders in books or online, you should try to figure them out yourself first. Design a decoder that selects between 8 output lines. That is, it will place a 1 on one and only one of the output lines at a time, depending on the inputs. Label the output lines O0, O1,..., 07. You can think of the input lines as comprising a binary number that corresponds to the subscript (the address) of the output line to be selected. Thus, an input of 110 would cause the decoder to put a 1 on 06. (a) How many input lines are needed for the decoder? (b) How many columns would a truth table have to have to completely characterize the decoder? (c) How many terms (products) would the sum-of-products have for the expressions representing each output? (d) Show the circuit in the decoder that computes the output 06. (e) Would a PLA be a good choice to implement a decoder? In general, how would you implement a decoder using a PLA?