Assume bit errors are mutually independent and identically distributed, each occurring with positive probability P <<1.

a) Find the even parity bit of the eight-bit message 11010011.

b) Derive the probability of error detection of an arbitrary m-bit message using 1 bit parity, where m is even.

c) Find the two-bit checksum of message 11010011 by simple XOR summation of consecutive two-bit message components.

d) Derive the probability of error detection of an arbitrary 2m-bit message using two- bit checksum of (c). You can apply the answer to (b).