Digital Logic Tutorial

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.
  • 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.
• A 4 bit multiplexer. I mux ask you: which should we select?
• A simple ALU (Arithmatic / Logic Unit)

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++

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.

See also:

• 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.

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