Is there any place (or book) where all the basic logic gates and their applications (including adders, half adders, multiplexers, demultiplexers, bit counters, flip flops, etc) are fully explained? This is the subject sometimes called "combinatorial logic".

Just to be clear here I am not interested in TTL components here; I just want to know the logic. In other words I do not explanations of PN junctions etc etc.

I keep seeing "lectures" that describe a few logic gate schematics here, a few circuits there, but do not comprehensively describe every logic gate and every simple machine (adders etc). For example, if you do a book search on "combinatorial logic" on Amazon you will find there are no books at all on the subject.


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  • 1
    \$\begingroup\$ Have you tried the datasheets of the devices in question? \$\endgroup\$ – Ignacio Vazquez-Abrams Jun 26 '16 at 10:31
  • \$\begingroup\$ @IgnacioVazquez-Abrams The question is not about devices, it is about logic. \$\endgroup\$ – Tyler Durden Jun 26 '16 at 10:41
  • \$\begingroup\$ You can look for books on "digital electronics". \$\endgroup\$ – Roger C. Jun 26 '16 at 10:58
  • \$\begingroup\$ @RogerC. I have Hill & Horowitz and also many other books. The problem is that these books are on ELECTRONICS not logic, so their discussions of combinatorial logic gates is always lacking and incomplete. They introduce a few gates, then immediately go into mapping and then other topics that have nothing to do with logic. \$\endgroup\$ – Tyler Durden Jun 26 '16 at 11:25
  • \$\begingroup\$ Perhaps you would have more luck searching for information on "Boolean Algebra" rather than "Logic Gates". The former is the principles used, the latter are electronic structures. \$\endgroup\$ – Tom Carpenter Jun 26 '16 at 17:37

Try "Experiments in Digital Principles" by Donald P. Leach. I think it will answer most of your questions.

From the table of contents:

  • Logic invertor
  • or, and, nor and nand gates
  • boolean algebra
  • 4-input multiplexer
  • 1-of-4 decoder
  • bcd to decimal decoder
  • xor gates
  • adders
  • multiplexers adder-substracter
  • flip-flops
  • shift registers
  • counters

And many more interesting subjects.

  • \$\begingroup\$ That looks like it might be a good resource, but I could not find that book for sale either on Amazon or ABE Books, so how would I get it? \$\endgroup\$ – Tyler Durden Jun 26 '16 at 11:31
  • \$\begingroup\$ Googling the book title immediately shows it is available on Amazon for as little s 20 cents. \$\endgroup\$ – Barry Jun 26 '16 at 11:35
  • \$\begingroup\$ I think I did not find it the first time because you mispelled the title and I copied and pasted it. \$\endgroup\$ – Tyler Durden Jun 26 '16 at 11:46
  • \$\begingroup\$ principal prɪnsɪp(ə)l adjective: first in order of importance; main. principle prɪnsɪp(ə)l noun: a general scientific theorem or law that has numerous special applications across a wide field. Spelling matters! Edit required! \$\endgroup\$ – Transistor Jun 26 '16 at 12:58
  • \$\begingroup\$ @transistor Yes, I corrected the title. I did a search on Amazon before posting my answer (it would be pointless to promote a book that's unavailable) but then typed it wrong here. It happens. \$\endgroup\$ – JvO Jun 26 '16 at 17:31

It seems you're looking for the contents of any basic book about digital electronics design. Seriously, you can pick any one of them.

But allow me to suggest Structured Computer Organization by Andrew Tanenbaum. While not being a book about digital circuit design (it is actually a book about how computers work, from bare-metal hardware to assembly language), it contains a very clear explanation of the basics of digital logic.

  • \$\begingroup\$ That book does not discuss combinatorial boolean logic. \$\endgroup\$ – Tyler Durden Jun 26 '16 at 11:28
  • 1
    \$\begingroup\$ Actually, it does, even if in a basic way (check Chapter 3). Perhaps you're looking for something more advanced (ASIC design oriented). In that case SCO is certainly not enough. \$\endgroup\$ – Electrical Architect Jun 26 '16 at 11:33
  • \$\begingroup\$ As I said in my question, I am interested in comprehensive treatment. See JvO's answer for what I am looking for. \$\endgroup\$ – Tyler Durden Jun 26 '16 at 11:44

I can recommend very much

"Digital Design and Computer Architecrure" by Harris and Harris

It's the best text book on that subject I know. The first 3 chapters cover quite well what you are looking for:

  1. From Zero to One
    1.1 The Game Plan
    1.2 The Art of Managing Complexity
    1.3 The Digital Abstraction
    1.4 Number Systems
    1.5 Logic Gates
    1.6 Beneath the Digital Abstraction
    1.7 CMOS Transistors
    1.8 Power Consumption
    1.9 Summary and a Look Ahead, Exercises, Interview Questions

  2. Combinational Logic Design
    2.1 Introduction
    2.2 Boolean Equations
    2.3 Boolean Algebra
    2.4 From Logic to Gates
    2.5 Multilevel Combinational Logic
    2.6 X’s and Z’s, Oh My
    2.7 Karnaugh Maps
    2.8 Combinational Building Blocks
    2.9 Timing
    2.10 Summary, Exercises, Interview Questions

  3. Sequential Logic Design
    3.1 Introduction
    3.2 Latches and Flip-Flops
    3.3 Synchronous Logic Design
    3.4 Finite State Machines
    3.5 Timing of Sequential Logic
    3.6 Parallelism
    3.7 Summary, Exercises, Interview Questions

The other chapters are:
4. Hardware Description Languages
5. Digital Building Blocks
6. Architecture
7. Microarchitecture
8. Memory Systems


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