A string of 0s and 1s is to be processed and converted to an even-parity string by

Chapter 2, Problem 68

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A string of 0s and 1s is to be processed and converted to an even-parity string by adding a parity bit to the end of the string.(For an explanation of the use of parity bits, see Example 30 in Chapter 9.) The parity bit is initially 0. When a 0 character is processed, the parity bit remains unchanged. When a 1 character is processed, the parity bit is switched from 0 to 1 or from 1 to 0. Prove that the number of 1s in the final string, that is, including the parity bit, is always even. (Hint: Consider various cases.)

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