COROLLARY THEOREMS - ELECTRONINC DESIGN NOTES: Logic Gates

ELECTRONIC DESIGN NOTES #11

Logic Gates

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Just 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.

The basic structure employed to present Logic Gates is:
1. OR, AND, and NOT Gates
2. NAND and NOR Gates
3. XORt Gates
4. More Gates Features

NOTE
The basic notions highlighted in this page are related to electronic design topics presented in the first part Hardware Design of Learn Hardware Firmware and Software Design.

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 with A and B, and the output is (generally) marked as C. The point to remember is, C is the result of a Boolean function.

AND, OR, NOT, LOGIC GATES

Picture

Truth Table

Description

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

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

A	A
1	0
0	1

Fig 3: NOT Gate

The output A is:

A = A

NAND AND 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 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

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

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

XOR GATES

The XOR Gate is presented separately, because we discovered few books where this Gate is incorrectly explained. 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

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

MORE GATES FEATURES

Some Gates have an inhibit control pin--particularly the NOT ones. That is a very nice and useful feature.

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.

There are basic Gates built with expanders. An expander is an input pin implementing additional logic, thus making them even more versatile.

Gates acre commonly used to implement hardware time delay circuits. In addition, gates are used to set/reset hardware logic levels, and as clean pulse drivers.

To end this, there are basic Logic Gates Networks, built on ICs, as are the AND-OR-Invert Registers, and others. All Logic Gates are very useful basic modules, therefore this topic is developed a bit more in Electronic Design Notes 13.

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