Consider a system where three 3-bit numbers (i.e., values between 0 and 7) are transmitted. As an error detection mechanism, the sum of all three numbers (modulo 8 so it also fits into 3 bits) is also transmitted. For example, when transmitting 4, 5, and 2, the sum of 3 is transmitted (4+5+2=11 and 11 mod 8 = 3).

(a) What is the maximum number of bit errors that this mechanism is guaranteed to detect under all circumstances? Give an example of where the mechanism cannot detect an additional bit error beyond the number you answered.

(b) Discuss if you consider this error detection mechanism to be efficient and effective. If you think it works well, state why. If you think it does not work well, explain its shortcomings.