Suppose that a five-digit code consists of four digits and a check digit that is assigned so that the sum of the five digits is divisible by 8. Assume that the digits 0 through 8 may be used in the code. When the sum of the first four digits is already divisible by 8, assume that 0 is always selected for the check digit. Determine whether the following errors would be detected and explain why.
a. The first and second digits have been transposed.
b. The third digit was supposed to be a 0 but was recorded as an 8.
c. The fourth digit is recorded as a 1 rather than a 5.
d. The check digit is recorded as an 8.
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