I was thinking about making my own minimalist TTL CPU for fun and knowledge, when this question came to mind. Basically, if a 1-Bit Computer can only recognize 2 numbers, 0 and 1, doesn't that mean that the computer could only have 2 registers or instructions? Then, I found the Motorola MC14500B, which is a 1-bit computer that has 16 instructions, with 4 pins for opcodes. Is the MC14500B considered a "true" 1-bit computer, since it has more than 2 instructions, and if so, could I apply the same concept to internel registers where there are more than just 2, but the actual logic going on in the CPU and the memory works on 1-bit? This is a simple question that I need some clarification on, so thank you for your help!
Many 8-bit CPU architectures have instructions that consist of more than one byte. I see no reason why a 1-bit CPU could not similarly have some instructions that consist of multiple bits.
At a more general level: The "bit-ness" of a CPU typically only reflects the size of its registers. It's perfectly possible (and, indeed, quite common) for instructions, the address bus, and/or even the data bus to be different widths from registers.
Yes, you can have many more than 2 internal registers and still have a 1-bit datapath and data register width. So yes, the Motorola MC14500B is considered a true 1-bit microprocessor. Like most processors, its instructions are wider than its data. From your description, it sounds like you would need instructions wider than MC14500B instructions so those instructions would have room for the operand specifiers; each operand specifier wide enough to pick one register.
The Wikipedia "1-bit architecture" says
A 1-bit computer architecture is an instruction set architecture for a processor that has datapath widths and data register widths of 1 bit wide.
You might also consider a serial computer architecture, like every computer built before 1951, which relaxes one requirement and allowing data register widths much wider than 1 bit, but keeps the datapath widths 1 bit wide. Those computers were necessarily very minimalistic because of the high cost of tubes, relays, and transistors at the time.
Good luck on your TTL CPU.