Lecture 5: Designing Circuits and operations and their gates (2)

28.06.12
2. OR GATE

http://sub.allaboutcircuits.com/images/04107.png

OR gate, so-called because the output of this gate will be "high" (1) if any of the inputs (first input or the second input or . . .) are "high" (1). The output of an OR gate goes "low" (0) if and only if all inputs are "low" (0). 

A two-input OR gate's truth table looks like this:

http://sub.allaboutcircuits.com/images/04108.png

3. NOT GATE

[EDITED] http://sub.allaboutcircuits.com/images/04154.png

NOT Gate is also known as Inverter, it reverses or 'invert' the input given. In digital circuits drawing its drawn as 'small circle'. That circle in the NOT-gate symbol is called an inversion bubble. A bubble on the input or output wire of another circuit symbol indicates an inversion of that signal: 0 becomes 1, and 1 becomes 0.

Some Booleen functions have identical truth tables therefore their logic circuits serves identical purposes; but one may be preferable to the other. To do this more useful logic gates are created. The following gates NAND, and NOR were created for this purpose.

4. NAND GATE

A variation on the idea of the AND gate is called the NAND gate. The word "NAND" is a verbal contraction of the words NOT and AND. Essentially, a NAND gate behaves the same as an AND gate with a NOT (inverter) gate connected to the output terminal. To symbolize this output signal inversion, the NAND gate symbol has a inversion bubble on the output line. The truth table for a NAND gate is as one might expect, exactly opposite as that of an AND gate: 

http://sub.allaboutcircuits.com/images/04106.png

As with AND gates, NAND gates are made with more than two inputs. In such cases, the same general principle applies: the output will be "low" (0) if and only if all inputs are "high" (1). If any input is "low" (0), the output will go "high" (1). 

We can see that equivalent AND gate circuit (which works same as NAND gate circuit) can be constructed with one two-input AND gate and then affixing one NOT gate on its output.

5. NOR GATE

The NOR gate is an OR gate with its output inverted, just like a NAND gate is an AND gate with an inverted output.

NOR gates, like all the other multiple-input gates seen thus far, can be manufactured with more than two inputs. Still, the same logical principle applies: the output goes "low" (0) if any of the inputs are made "high" (1). The output is "high" (1) only when all inputs are "low" (0).

We can see that equivalent OR gate circuit (which works same as NOR gate circuit) can be constructed with one two-input OR gate and then affixing one NOT gate on its output. 

• REVIEW:
• Rule for an AND gate: output is "high" only if first input and second input are both "high."
• Rule for an OR gate: output is "high" if input A or input B are "high."
• Rule for a NAND gate: output is not "high" if both the first input and the second input are "high."
• Rule for a NOR gate: output is not "high" if either the first input or the second input are "high."

(This portion of tutorial is taken from|allaboutcircuits.com)

Next topic: 29.06.12: Lecture 6: Logic Circuits(1): Building Boolean Expressions

Previous topic: 26.06.12: Lecture 4: Designing Circuits and operations and their gates (1)