28. [12/14 Points]
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A digital system you are designing needs to transmit 2-bit binary numbers along a transmission line, but it's an electrically noisy environment, bad enough to cause "bit flips". So, to detect corrupted data, each 2-bit number XY is accompanied by a third
bit P, with P being set (made =1) or reset (made =0) so the number of 1's in each 3-bit packet XYP is always an odd number. When the packet is received, a logic circuit sets an error signal E if the number of 1's in the received packet is even, because the
only way that could happen is if a bit got flipped due to noice somewhere in the transmission. The P stands for "parity bit", and this technique is commonly used in digital communication systems to detect corrupt data packets and bad connections.
(a) Create a truth table for P, the third bit added at the transmitter end of the data link, so that each packet XYP has an odd number of ones.
XY P
0 0 1
0 1 0
1 0 0
1 1 1
(b) Draw a logic circuit that has two inputs (labeled X and Y) and one output (P), that reproduces the correct truth table above. Scan or take a picture of your drawing to upload. (Acceptable file types are jpg, gif, png, pdf or doc.)
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(c) Create a truth table for E (the error signal) given input XYP at the receiver end of the data link, set if there are an even number of 1's in XYP.
XY P E
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 0
(d) Draw a logic circuit that has three inputs (labeled X,Y and P) and one output (E), that reproduces the correct truth table above.
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