If you want to start an argument at a Hackaday meeting, you have only to ask something like “How much does this weigh?” or “What time is it?” But if you really want to start a street brawl, you can always say, “Are these numbers random?” Making random numbers that are actually random is actually a tough nut to crack. Most of what we do is, technically, pseudo-random (but we’ll say random number and assume you know what we mean). One way to generate seemingly random sequences is to use a linear feedback shift register or LFSR. You can use LFSRs in software, but they are also very useful in hardware design and [Adam Taylor] takes us through his use of them on FPGAs in a recent post.
As [Adam] points out, they not only generate random-like patterns but they are often used as high-performance counters and in error detection and correction schemes. As the name implies, the mechanism is a simple shift register with one or more of its outputs fed back around to the input. How can that be random? Well, it can’t be, but it is often good enough for places where you need a sequence of numbers. Depending on how you organize the outputs — or taps — and how you feed them back means you can control the pseudo-random sequence.
A Fibonacci LFSR
There are two common methods for creating LFSRs. A Fibonacci-style design uses XOR (or inverted XOR) gates in the feedback loop. For example, consider an eight-stage counter. The post shows the output of flip flop 4, feeding an XOR gate that drives the counter’s input. The other input of the XOR ..
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