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ELECTRONIC DESIGN NOTES #11 - LOGIC GATES


LEARN HARDWARE FIRMWARE AND SOFTWARE DESIGN 5TH EDITION - FRONT COVER
RED LEAF R


Just a few years ago, logic gates were regarded as the most advanced products in digital electronics. Today things went far, far ahead. The old knowledge about logic gates, however, is still very important for hardware designers. If you want to become a true specialist in hardware design, you need to start with the very roots, with the history of things.

The interesting aspect about logic gates is, they work exactly the same in hardware and in firmware. In other words, you can build logic gates circuits in firmware, and they will work just as the hardware ones do, except for being a bit slower in execution speed, naturally.

The structure employed to present (summarily) logic gates in this page is:

1. OR, AND, NOT Gates
2. NAND, NOR Gates
3. XOR Gates
4. More Gates Features


NOTE

The basic notions highlighted in this page are related to a few electronic design topics presented in the first part, Hardware Design, of
LEARN HARDWARE FIRMWARE AND SOFTWARE DESIGN.

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1. OR, AND, NOT GATES

A gate is a logic circuit performing one, simple Boolean function. Because they are used a lot, there are standard families of gates-- this topic is going to be presented in Design Notes #13.

Logic gates are presented here one at a time. To start, please be aware that logic gates come as 2, 4, 6, or more similar gates packed into one IC. Conventionally, pin 14 is wired high to VCC, and pin 7 is grounded.

The (electrical) input logic signals are marked in this page by A and B, and the output is (generally) marked as C. The point to remember is, the output C is the result of a Boolean function.
 

AND, OR, NOT, LOGIC GATES

Picture Truth Table Description
AND Gate
A B C
0 0 0
0 1 0
1 0 0
1 1 1
Fig 1: AND Gate

The output C is:

        C = A * B
OR Gate
A B C
0 0 0
0 1 1
1 0 1
1 1 1
Fig 2: OR Gate

The output C is:

        C = A + B
NOT Gate
A A
1 0
0 1
Fig 3: NOT Gate

The output A is:

        A = A

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2. NAND, NOR GATES

NAND and NOR gates are the most used gates in logic circuits. It may be interesting to note that both of them implement the NOT function, in addition to AND/OR: that is due to the fact they were built out of NPN transistors (the silicon type). Fact is, the NAND and NOR gates were the first ICs used to implement Combinational Logic Networks.
 

NAND, NOR LOGIC GATES

Picture Truth Table Description
NAND Gate
A B C
0 0 1
0 1 1
1 0 1
1 1 0
Fig 4: NAND Gate

The output C is:

     C = A * B

The NAND gate is equivalent to an OR gate having negated inputs
NOR Gate
A B C
0 0 1
0 1 0
1 0 0
1 1 0
Fig 5: NOR Gate

 The output C is:

     C = A + B

The NOR gate is equivalent to an AND gate having negated inputs
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3. XOR GATES

The XOR gate is presented separately because we have discovered a few books in which this gate is explained incorrectly. The XOR gate it is one of the most important, therefore it is mandatory to understand it very well.
 

XOR LOGIC GATE

Picture Truth Table Description
XOR Gate
A B C
0 0 0
0 1 1
1 0 1
1 1 0

Fig 6: XOR Gate

The output C is:

     C = A*B + B*A

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4. MORE GATES FEATURES

1. Some gates have an inhibit control pin--particularly the NOT ones. That is a very nice and useful feature.
2. Some gates have a strobed input. If the strobe input is HIGH, the gate will function normally; if the strobe is LOW, the output of the gate will remain in its last state.
3. There are basic gates built with expanders. An expander is an input pin implementing additional logic, thus making the gate even more versatile.
4. Gates are commonly used to implement hardware time delay circuits. In addition, gates are used to set/reset hardware logic levels, and as clean pulse drivers.
5. To end this, there are basic logic gates networks, built inside ICs, as are the AND-OR-Invert Registers, plus many others. All logic gates are very useful basic modules, therefore this topic is developed again in Electronic Design Notes #13.

 


LHFSD - Front Cover
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