Linear Feedback Shift register of size 2^7

[Weaver]

Homework Statement

The student decides to use a Linear Feedback Shift Register (LFSR) to
repeatedly step through each row of memory when performing DRAM
refresh. The memory has 2^7 rows. Design an LFSR circuit to perform this task.

Relevant Equations

[See table below]

From this table:

• Looking at the 7 row and taking the first entry, 1
• This is 000001
• Adding back the highest and lowest bit: 10000011
• And then the equation would just be x^7 + x +1 ?

• Or taking the taking the third entry, 7
• This is 000111
• Adding back the highest and lowest bit: 10001111
• And so the equation is just :x^7 + x^3 + x^2 +x+ 1?

Is that correct?

 

[Baluncore]

Is that correct?

There is a trap for beginners with LFSRs, either the case of all ones, or that of all zeros is prohibited as the register locks if it enters that state.

An SFSR must be initialised to avoid an attempted start from the prohibited state.

What would happen if you used only 7 bits from an 8 or 9 bit maximal length LFSR, would that generate all 7 bit states equally from 0000 000X to 1111 111X ?