An algorithm to implement a boolean function as a gate network using only NAND's or only NOR's is presented. Any boolean function can be implemented straightforwardly using AND's, OR's, and NOT gates. Using DeMorgan's Law in different forms gates in the network can be successively converted to use only NAND's or only NOR's.
NAND's and NOR's are the most common basic logic circuit element in use because they are simpler to build than AND and OR gates, and because each is
logically complete . Many logical functions are expressed using AND's, OR's, and Inverters (NOT), however, because an implementing circuit can be constructed straightforwardly from the truth table expression of a logical function and because
Karnaugh Map's can be used to minimize AND, OR, INVERTER networks.
This document is adapted, with permission, from algorithms and examples given in
Dr. Jump's Elec326 course notes.
Below a simple algorithm is given for converting a network with AND gates, OR gates and INVERTERS to one with NAND gates or NOR gates exclusively. First the boolean function is represented using AND's, OR's, and NOT gates. Then, using DeMorgan's Law in various forms, the AND, OR, INVERTER network is converted step-by-step to use only NAND gates or only NOR gates.
Demorgan's law using boolean algebra
OR to NAND
AND to NOR
$a\vee b\equiv \neg (\neg a\wedge \neg b)$
$a\wedge b\equiv \neg (\neg a\vee \neg b)$
Conversion algorithm
Draw AND, OR, INVERTER implementation. First draw out an implementation of the boolean function using AND gates, OR gates and INVERTERS. Any implementation that uses only those three gate types will work. One way to implement a boolean function using AND's, OR's and INVERTERS is to build the
Disjunctive Normal Form of the boolean function from the truth table that describes the function. Disjunctive Normal Form, is also called
Sum of Products form.
Propositional Logic: Normal Forms gives a succinct treatment of normal forms and of how to go from a truth table to Disjunctive Normal Form.
Apply DeMorgan's Law. Apply DeMorgan's Law to the circuit by using the equivalences in the first two rows of the Figure above. To create a NAND only circuit, use the transforms in the left box, and for a NOR only circuit use the transforms in the right-hand box.
Remove redundant inverters: Any time that two inverters are in series (an inverted output goes directly in to an inverted input), remove both of them, since they cancel each other out.
Replace remaining inverters. Replace any remaining inverters with the equivalent NAND or NOR implementation (the third row of the Figure).
Note that in step c. the final elimination of inverters isn't quite done since B and D are inverted into one of the NAND's.
Questions & Answers
find the 15th term of the geometric sequince whose first is 18 and last term of 387
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.