仅用与非门合成左移 1 位？

Question

I have an algorithm that performs division of 2 64-bit unsigned integers using C bitwise operators (<<, &, ^, |, ~) in a loop.

Now I would like to eliminate shift left << operator completely to understand how this is done as I can already synthesize AND, OR, XOR, NOT using NAND gates.

Is it possible to perform left shift by 1 with JUST NAND gates too? I have read a little about flip-flops in electronics but I'm implementing this in pure software just to understand it.

I want to avoid using << or >> operators completely and do not want to use existing arithmetic operators from any computer language including assembly.

Answer 1

In hardware, you can implement left shift by 1 without any logic gates at all. Just wire the data lines like so:

If you want something more generic, you could implement a barrel shifter . This can be synthesised from multiplexers:

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which in turn can be synthesised from NAND gates.

Here is a comprehensive master's thesis on the subject: Barrel Shifter Design, Optimization, and Analysis .