Output of a Linear Shift Register given Plaintext and intial state Given an initial state $S_0 = (0101)$ and plaintext $P = 1010101011$ I need to find the ciphertext.

The method to solve this was not taught in my coursework, and the information I have found online does not seem to apply to this.

Can anyone explain the steps needed to solve this?
Read the drawing assuming:


each of the four (about) square boxes $a_j$ initially (at $t=0$) holds one of the four  bits of $S_0$ (in reading order, unless otherwise stated);
information follows arrows (almost) instantly, except when getting into a square box where that is delayed until $t$ has grown by $1$ (in time unit or clock period); notice this implies that the content of the left square box is also (with negligible delay) on the arrowhead going straight down and the one going right-down;
there are three implicit short arrows between the four square boxes, oriented as the rightmost arrowhead;
each $\oplus$ symbol performs the exclusive-OR of all the ingoing arrows, and outputs that result to outgoing arrow, with no significant delay;
the plaintext bits are made available one by one (starting at $t=0$, and in reading order, unless otherwise stated) on the input side of the arrow marked "plaintext";
the ciphertext bits are what's at the arrowhead marked "Cipher-text" (with the same convention as for plaintext).


You can now manually compute what there is in each of the boxes, arrowheads, "plaintext", "Cipher-text", at any integer value of $t\ge0$ (or, more precisely, shortly after). Assuming increasing time matches reading order, you might want to format this as a table with $t$ increasing from left to right, so that the lines with "plaintext" and "Cipher-text" will contain the plaintext and ciphertext in reading order.