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Here are two examples of an 8 bit XOR LFSR with a 1, 2, 3 and 7 tap configuration allowing for a maximal length output of pseudo random number sequences. An 8 bit binary sequence configuration can represent any number from 0 to 255, however a close examination of the operation of each XORed LFSR makes it clear that the initial condition where all register bits are 0 is not allowed since it would send the register into a endless 0 loop. Any non zero state is therefore required for the initial startup and operation of the XORed LFSR. The LFSR will therefore cycle through all binary configurations between 1 and 255 before repeating the sequence.
The bottom configuration is called a many-to-one LFSR, XOR tapped at 1, 2, 3, and 7 In this configuration, the LSB (least significant bit) is XORed with the output of the 4th flip flop, the output of flip flops 2 and 3 are XORed together and the former and latter outputs are XORed together using 2 level combinations logic, the final result of which is fed into the register via the MSB (most significant bit). The LFSR will cycle through all binary configurations in a pseudo random manner before repeating the sequence.
An alternate configuration can be seen with the top function is called a one-to-many LFSR. Here we have the XOR gates tapped at 1, 2, 3, and 7 as below, however they are tapped in sequence with the bits of the register. This function has the output fed directly back into the register while being individually XORed with the output of flip flops 2, 3 and 4, the results of which are fed into the input of the following flip flops. This configuration avoids the need for higher levels of logic and provides for higher clocking speeds and faster operation. Again, this LFSR function will cycle through all binary configurations between 1 and 255 in a pseudo random before repeating the sequence.
Close the switch to start.
Note the logic source is present for manual clocking and to prevent floating components while the switch is open.
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