Digital Logic Tutorial

The logic power of computers and even micro-controllers today is mind boggling, but even more amazing to me is that all of the functions (every one) of the biggest computer can be shown in terms of one simple logic gate: The NAND. Every part even Memory: From the BIT to the Giga Byte, Math: From the most basic Addition to the most complex Floating Point calculation, Decision making: If not real reasoning, Input and Output are all built from this one tiny and very simple atomic unit of logic!

In these pages my son Remy and I will start to show you how computers actually work and how simple (and complex) they really are.

Contents

• The NAND or "Not AND" The amazingly simple basis of all computing
  • And how NANDs can make all logical decisions, including:
  • XOR and XNOR, which  tell us if numbers are different or equal
• RS Flip Flop How computers learn and remember
  • although the D Flip Flop is a bit closer to a bit.
  • the register can hold a number
  • and the T Flip Flop ticks out time
• Binary and Decimal Numbers Count like a computer
• Binary Addition Circuit NANDs can Add! A little bit anyway.
  • Binary Full Adder carriess us into blocks
  • Binary Multidigit Adder but NAND adders can really add.
  • Binary Subtractor and subtracting is NOT adding (plus a bit)
• A 2 bit to 4 line active low decoder Stepping through a sequence.
  • In any order, it's quite arbitrary!
  • ROM and PROM and MicroCode, oh my!
• Sequences count.
• A 4 bit multiplexer. I mux ask you: which should we select?
• A simple ALU (Arithmatic / Logic Unit)
• RAM
• A microscopic micro

Next

How a very simple little "gate" or elemental bit of logic is the basis of all computing. It's just Not this AND that.

Also:

• Bitwise operations in C/C++
• Neural Networks

This series makes use of a program written by Andreas Tetzl of tetzl.de that makes the NAND gate, and the things we build from it, come alive on your screen. It is called LogicSim and it is a digital logic simulator that can work from a web page. If we did not have LogicSim, we could only tell you how it all works and could not show you. To use LogicSim, you must have Java^tm from Sun Micro systems. You can check if you have Java on their web page at java.com. Look for the "Do I have Java?" link. Once you have Java, you may need to enable it in your browser. For Google Chrome, see the CheerpJ Applet Runner

See also:

• https://circuitverse.org/simulator Very nice online logic simulator. Must register to use, but free.+
• https://www.peterhigginson.co.uk/ Scroll down and follow the links to find 3 different levels of processor simulators which operate online and books to learn how they work. A very small "Little Man" (hard to find) with 16 instruction, a RISC ARM and a full ARM simulator. Very well done.+
• http://8bitworkshop.com/v3.3.0/?platform=verilog&file=clock_divider.v Emulates FPGAs, with many examples, including complete CPUs and older game systems, all in the browser. You can code on the left and see the results on the right.+
• https://hdlbits.01xz.net/wiki/Main_Page Learn the Verilog language for Digital Logic via a series of puzzles. You can login to keep your scores and share your progress.+
• http://nandgame.com/ From NAND to CPU.+
• https://www.robotodyssey.online/ FANTASTIC robot / logic game with really crappy graphics. Use the mouse instead of the arrow keys, click instead of spacebar. Still have to use "R", "S", "T" and "C" but it's much easier with the mouse. Wonderful work by "scanlime" (Micah Elizabeth Scott)
  https://github.com/scanlime/robot-odyssey-rewired Source+
• https://www.zybooks.com/catalog/digital-design/ A "digital book" with interactive lessons (and less text).
• https://eater.net/8bit/ Brilliant series with many videos to show each part as it's built on a breadboard.
• http://hackaday.com/2016/03/25/crawl-walk-run-a-starter-cpu/ +
• http://labs.domipheus.com/blog/designing-a-cpu-in-vhdl-part-1-rationale-tools-method/ Designing a CPU in VHDL+
• http://hackaday.com/2016/03/16/crawl-walk-run-planning-your-first-cpu-design/ +
• https://hackaday.io/project/9795-nedonand-homebrew-computer Computer made entirely from NAND TTL chips.+
• http://www.edaplayground.com/ Edit and test Verilog or VHDL code in your browser.+
• https://github.com/cesarares/Logic-Sim An HTML5 digital logic simulator! Please consider supporting the translation of this tutorial into the format of this new simulator.+
• http://mikejmoffitt.com/wp/?p=238 Writing a software version of a CPU to understand what is going on under the hood. Useful, but totally misses the genius of how hardware accomplishes those actions.+
• http://www.ostracodfiles.com/basic/menu.html An 8 bit TTL computer made from only 10 chips and an EEPROM. There are two registers (A and B) and a PC. Amazingly enough, it can do useful work with only 2 instructions: MNZ will copy data from source to destination only if A register is not zero. ADD will add source and A register then store the result in destination.+
• http://www.bigmessowires.com/category/nibbler/ A 4 bit computer design entirely from 7400 series logic chips.+
• http://dl.dropbox.com/u/1252290/Tic%20Tac%20toe.pdf Tic-Tac-Toe game made from logic circuits.+
• http://www.nand2tetris.org/ "The site contains all the software tools and project materials necessary to build a general-purpose computer system from the ground up. We also provide a set of lectures designed to support a typical course on the subject."+
• http://ygg-it.tripod.com/index.html A 4 bit computer from discrete logic and an old ALU chip.+
• http://tams-www.informatik.uni-hamburg.de/applets/hades/webdemos/index.html Another java based logic simulator.+
• http://www.instructables.com/id/How-to-Build-an-8-Bit-Computer/?ALLSTEPS How to build a complete working 8 bit computer from basic logic and memory chips. Not for the faint of heart, especially if you use a whiteboard as does the author.+
• http://www.saccade.com/writing/projects/CS428/WireWrap.html Really nice page about a college project to build a calculator and then a computer from TTL logic chips. This is back when people actually understood how computers work ,o)+
• http://ozark.hendrix.edu/~burch/logisim/ LogiSim (not LogicSim) is another very powerful logic simulator commonly used for instructional purposes. It is somewhat less graphically appealing than LogicSim.
  • http://elearning.cizgi.com.tr/logisim.aspx
• http://ozark.hendrix.edu/~burch/socs/hymn/
• http://www.sontrak.com Logic Friday is a freeware tool for students, hobbyists, and engineers which allows them to:
  • Enter a logic function as large as 16in x 16 outas a truth table, an equation, or a gate diagram
  • Minimize a function quickly or exactly, compare functions, and generate new functions as logical combinations of others
  • Automatically generate a multi-level minimized gate diagram using gates chosen from a library
  • View any function as a truth table, equation, or gate diagram and trace the state of each gate's outputs for a given input
  • Generate efficient, compact C code lookup functions from logic functions
  • Save functions and gate diagram images to files, export and import truth tables as CSV files.