In college, I took a computer architecture course that briefly went into CPU microcode. The fake CPU we studied divided opcodes into bit fields where a certain

In college, I took a computer architecture course that briefly went into CPU microcode. The fake CPU we studied divided opcodes into bit fields where a certain bit caused a certain primitive operation, like maybe triggering an adder. From this you could see that a specific opcode was just a particular composition of the right primitives. "Valid" opcodes were simply the combinations that were useful enough to document, and "invalid" ones were superfluous or meaningless combinations. Once you understand this, illegal/invalid/mystery opcodes are a lot less surprising; rather, they're inevitable. I was also taking a logic course at the time and dreaming in terms of truth tables, so it was quite a formative time in my early understanding of processor architecture.