1. The Voting Game How do we overcome transmission errors?

2. Vote for your favorite animals: AnimalCode Alligator000 Butterfly001 Cat010 Dog011 Elephant100 Frog101 Gorilla110 Other111

3. Error can occur during the transmission. In digital transmission, error means: 1  0, or 0  1. What would happen if one of the “bit” you entered in your vote is affected by transmission error? What can we do to so that our votes won’t be incorrectly registered? AnimalCode Alligator000 Butterfly001 Cat010 Dog011 Elephant100 Frog101 Gorilla110 Other111

4. What if we add one extra bit to the codes? Notice the “sum” of all digits in each code is always an even number This kind of error detection code is called Parity Check. Use some math – of course! AnimalCode Alligator0000 Butterfly0011 Cat0101 Dog0110 Elephant1001 Frog1010 Gorilla1100 Other1111 Now see what happens if one of the bits we entered is affected by transmission error?

5. Can parity check code detect any errors? No. If there are even number of bits affected by the error, the parity check won’t detect it. But having two-bits error is much less likely to than one- bit error. Parity check can greatly reduce the chance of our votes being incorrectly received. We can design more complicated codes to detect multi- digit errors, or even correcting the error. But more bits need to be added. 0101 0xx100110011CatButterfly AnimalCode Alligator0000 Butterfly0011 Cat0101 Dog0110 Elephant1001 Frog1010 Gorilla1100 Other1111

6. If the probability for each bit to be affected by error is 1/10, what is the probability that our vote will not be correctly registered without parity check? Probability Analysis: 1-(9/10)*(9/10)*(9/10)=0.271 If the probability for each bit to be affected by error is 1/10, what is the probability that our vote will not be correctly registered with parity check? (two bits error)+(4 bits error)=

7. Without parity check: 0.271 = more than 1 out of 4 times our vote will be registered incorrectly. With parity check: 0.0478 = less than 1 out of 20 times our vote will be registered incorrectly. Chance of error is greatly reduced. Math did it again!