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1. Create an ordered list for the binary digits 0000 thru 1111 (i.e. decimal 10

ID: 3568573 • Letter: 1

Question

1. Create an ordered list for the binary digits 0000 thru 1111 (i.e. decimal 10 thru 15),such that only one bit changes per step. 2. Completely separate but nevertheless also using four binary digits, devise a scheme, algorithm, template, plan, circuit, etc, such that a four bit binary message will be received and decoded accurately enough though one of the bits may have been garbled. For example, suppose the intended four bit message was meant to be 0 1 10. If at most, one of the bits had been garbled, the possible received bits may have been any of the following: 0 1 1 0 = no error 1 1 1 0 = first bit garbled 0 0 1 0 = second bit garbled 0 1 0 0 =third bit garbled 0 1 1 1 = fourth bit garbled How could the receiver know if a bit had been garbled, and if so, which one? Note: Your algorithm should also work for any four binary bit message. For example, if 1 1 1 1 were received; is this the correct message? If not, what was the intended message?

Explanation / Answer

1. Desired Ordered List:-

0000

0001

0011

0010

0110

0100

0101

1101

1100

1000

1001

1011

1010

1110

1111

2.) The best algorithm would be to send each bit 3 times to the receiver. The receiver will receive 12 bits altogether. if a bit is incorrectly received the receiver asks for that bit again.

Lets say the message is 0101.

The sender sends 1(Least significant bit) three times to the receiver. If the receiver gets all 3 1's,the receiver knows the bit is correctly received and no error was there.

The receiver asks for the next bit. The sender sends 0 three times but the receiver gets 1 zero and 2 one's. The receiver knows this bit is incorrectly reeived and asks for the same bit again repeatedly until all 3 bits received have the same value.

Then the receiver asks for the next bit and so on.