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CRC 1 : Suppose that we want to transmit the message 1 0 1 0 and protect its from errors using the following CRC polynomial:

CRC1: Suppose that we want to transmit the message 1010 and protect its from errors
using the following CRC polynomial:
C(x)=x6+x5+x3+x2+x+1.
This CRC is used in GSM wireless networks.
(a) Using two methods i) polynomial division; and ii) binary coefficient division to
determine the message that should be transmitted.
(b) Draw the hardware using shift registers and XOR gates to implement the CRC
algorithm with the above C(x). Using the hardware, determine the CRC bits
and the message that should be transmitted.
(c) Suppose that the second leftmost bit of the message is inverted due to noise.
What is the result of the receiver's CRC calculation? How does the receiver know
that an error has occurred?
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