One way to help ensure that data are communicated

Chapter 7, Problem P7.76

(choose chapter or problem)

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 P7.76 produces the correct parity bit P for the nibble (fourbit 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 1s 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. A B C D P Figure P7.76