I'm happy to say that I'm uniquely qualified to help you.
I have a BS in Computer Engineering and a MS in Electrical Engineering, with a specialty in VLSI and microelectronics.
While in school, I had to design a microprocessor, one transistor at a time. Great experience, by the way.
I will summarize this process from a Top-Down approach, in case you're a CS major. (Note that engineering is Bottom-Up!)
- C/C++ gets converted into Assembly Language.
- Assembly Language gets converted into bytes.
(One or more bytes encode each machine instruction and data)
- Each machine instruction takes multiple clock cycles to execute.
- On each clock cycle, a "microcode" (a.k.a. Register Transfer Language) moves data around.
(The order in which data are moved from one register to another is controlled by a Finite State Machine.)
- Each finite state machine is composed of sequential circuits and combinational circuits: multiplexers, decoders, etc.
- Each sequential circuit is composed of some type of memory element : flip-flops, latches, etc.
(Sequential circuits can be static, quasi-static, or dynamic. In all cases, they are composed of combinational logic with feed-back.)
- Combinational logic is composed of CMOS (MOSFET) transistors. In the past, we used BJTs... and they're actually making a comeback.
- Transistors are arranged in such a way as to perform logic equations: Inverter, NAND, NOR, etc.
(Look up a CMOS Inverter to know what I'm talking about.)
Pretty easy, right!?!
I want to encourage you to look at the following references, in order.
(1) CMOS Digital Integrated Circuits by Kang and Leblebici --the best digital VLSI book ever
(2) Digital Logic Circuit Analysis & Design by Nelson et al. --tough book on digital logic, but pretty good
(3) Computer System Architecture by Morris Mano --works its way up from logic design (K-maps, etc.) to state machines to assembly language
And now, I'm going to through a curve ball at you: Any algorithm you can implement in software, you can also implement in hardware.
How is this possible? Hint: Think of Finite State Machines.
And then look into ASIC and FPGA design of digital filters and digital control systems.