Question: A decoder is a control circuit with n input lines and 2n output lines (numbered 0 through 2n - 1). The pattern of n bits on the input lines represents a binary number between 0 and 2n - 1. A decoder activates the output line with the corresponding identification number by putting a 1 output on that line and 0 outputs on all other output lines. A decoder in a computer can, for example, read input lines that represent a binary memory address and then activate the line to that memory cell for a read operation.

a. Write truth functions for a decoder where n = 2, that is, there are 2 input lines and 22 = 4 output lines (hence four truth functions).

b. Draw the logic network that incorporates all four truth functions.