LFSR

Inputs

Outputs

How It Works

A real die is honestly unpredictable. A digital circuit finds it easier to pretend: an LFSR is an 8-bit carousel of flip-flops where every tick the bits shift over, and XOR mixes the sum of several state bits into the freed slot. To the eye it looks like chaos, but inside it is strict mathematics.

The key property is determinism. The starting value 0x9C and the polynomial x⁸ + x⁶ + x⁵ + x⁴ + 1 pin down every next step: the new bit equals state[7] ⊕ state[5] ⊕ state[4] ⊕ state[3], and the remaining bits shift left. Example: 0x9C (156) → 0x39 (57) → 0x73 (115) — and so on through all 255 non-zero values in a row, after which the circle closes.

A nuance: the state 0x00 is a trap. XOR of all zeros is zero, and the register gets stuck there forever — so the seed must never be zero. The value is read like any I/O device of the course: IO_SEL = 1, DevAddr = 0x1A — port 0xFA.

Examples (clock sequence)

A dice roll from this sequence: LDA 250 reads the port, AND 7 trims it to 0–7, ADD 1 lifts it to 1–8.

Usage

Level 26 "Dice Roll" teaches reading the LFSR: LDA 250 puts a random byte into the accumulator, AND 7 trims it to the 0–7 range, ADD 1 lifts it to 1–8, and a conditional throw-away handles the extra values. In level 29 the food coordinates of Snake are born the same way: AND 15 yields a number from 0 to 15 — exactly the size of the playfield.

A concrete use: clock the LFSR on every Clock tick continuously, and read the port only at the moment of choice — then the "randomness" depends on which very tick the program peeked into the register. The same trick works for enemy behavior and any random events in games built on the course CPU.