One way to help ensure that data are communicated correctly is to append a parity bit to each data word such that the number of 1s in the transmitted word is even. Then, if an odd number are found in the received result, we know that at least one error has occurred.
a. Show that the circuit in Figure produces the correct parity bit P for the nibble (four-bit data word)ABCD. In other words, show that the transmitted word ABCDP contains an even number of 1s for all combinations of data.
b. Determine the minimum SOP expression for P in terms of the data bits.
c. If the received word contains a single bit error, the number of ones in the word will be odd. Draw a circuit using four XOR gates that outputs a 1 if the received word ABCDP contains an odd number of 1s and outputs a 0 otherwise.
