Chapter 18, Problem 43E

Explanation of Solution

Improvement of error detection using the check bits:

The individual digits in the number are added together and the unit digit of the result is called as check digit.

• It is used in error detection.
• The unit’s digit of that sum is stored with the number.
• The additional digit used along with the check digit is used to find out the transposition error.
• To find out the carry of an additional digit, unit’s digit can be found out by the sum of even digits in the number or by sum of odd digits in the number.

For example:

Consider the number: 6168-12.

• Here, 6168 is the required number and 1 is the check digit; “2” is the additional digit which represents the unit’s place of sum of the odd digit’s in a number.

If the number is received as 1668-12 instead of 6168-12 incorrectly, to ensure that the received number is correct, the check digit and additional digit are referred as follows:

• Step 1: Count the received number from left to right.

• Step 2: From the above diagram, the sum of digits produces the result as 21.
• Step 3: The unit digit of the sum “21” is considered as check digit and it is “1” which is same as that of the received number. So, the received number may not be corrupted and received as it is...