FULL ADDER design using lesser number of gates

Truth table for a full adder:
A       B       Cin      C       S
0        0         0        0       0
0        0         1        0       1
0        1         0        0       1
0        1         1        1       0
1        0         0        0       1
1        0         1        1       0
1        1         0        1       0
1        1         1        1       1

Generally,
S=A xor B xor Cin
Cout=AB+BCin+ACin
needs:
2 2 i/p xor gates
3 2 i/p and gates
1 3-i/p or gate

Another method
S=A xor B xor Cin
Lets solve the K-map for C differently

C=AB+Cin(A xor B)
needs
2 2 i/p xor gates
2 2 i/p and gates
1 2 i/p or gate

Since prop delay through any gate depends on :
type of gate , no.of i/p
therefore 2nd design may prove to be beneficial in some cases.

4-input NAND gate using 2-input NAND gates

Truth table for a 4-input NAND gate is as given below:

A       B       C       D        F
0        0        0       0        1
0        0        0       1        1
0        0        1       0        1
0        0        1       1        1
0        1        0       0        1
0        1        0       1        1
0        1        1       0        1
0        1        1       1        1
1        0        0       0        1
1        0        0       1        1
1        0        1       0        1
1        0        1       1        1
1        1        0       0        1
1        1        0       1        1
1        1        1       0        1
1        1        1       1        0


Simplifying K-map for the variable F,we get
F=A'+B'+C'+D'
=(A'+B')+(C'+D')
Using De-Morgan's theorem,we get
=(AB)'+(CD)'

The NAND circuit for this logic can be represented as:

4-input NAND GATE implementation using 2-input NAND GATES

MINTERM ,CANONICAL SUM OF PRODUCTS(SOP) and MINIMUM SOP

MINTERM:
A minterm is a product term that contains all the variables of a logical function either in true or inverted state.

A logical function is given:
F=AB'+C'

Its truth table is as below:

A  B C F
0 0         0        1
0 0 1        0
0 1         0        1
0 1         1        0
1 0         0        1
1 0         1        1
1 1         0       1
1 1        1        0

All the minterms that can be generated from the above given truth table are:

A'B'C' , A'B'C , A'BC' , A'BC , AB'C' , AB'C , ABC' , ABC

CANONICAL SOP:
It is an expression that describes a logical function from its truth table.A canonical SOP consists of the sum of all the minterms for which the function has a value 1...or the function is true.

For the same truth table as stated above ,the canonical SOP can be written as:
F=A'B'C'+A'BC'+AB'C'+AB'C+ABC'

MINIMUM SOP:
A minimum minterm is obtained by simplifying a canonical SOP. It provides a minimum hardware simplification of the logic function.
For the same truth table,the minimum SOP obtained after simplification is:

F=AB'+C'

"AND", "OR", "NOT" IMPLEMENTATION USING "NOR" GATE

Conversion of a NOR gate into a NOT gate, an OR gate and an AND gate is as shown below:

NOR IMPLEMENTATION

"AND", "OR", "NOT" IMPLEMENTATION USING "NAND" GATE

Conversion of a NAND gate into an AND gate ,a NOT gate and an OR gate is as shown below:

NAND IMPLEMENTATION

UNIVERSAL GATES

NAND and NOR are the universal gates.
AND , OR and NOT are fundamental gates,together they can  implement any digital logic.But NAND or NOR alone is capable enough to implement any digital logic,hence these two gates are called universal Gates.

Frequency Division Multiplexing And Wavelength Division Multiplexing

SIMILARITY BETWEEN FDM AND WDM

The term wavelength-division multiplexing is applied to an optical carrier (which is typically described by its wavelength), whereas frequency-division multiplexing applies to a radio carrier (which is more often described by frequency). Since wavelength and frequency are tied together through a simple directly inverse relationship, the two terms actually describe the same concept.

HOW FDM WORKS

At the source end, for each frequency channel, an electronic oscillator generates a carrier signal, a steady oscillating waveform at a single frequency such as a sine wave, that serves to "carry" information. The carrier is much higher in frequency than the data signal. The carrier signal and the incoming data signal (called the baseband signal) are applied to a modulator circuit. The modulator alters some aspect of the carrier signal, such as its amplitude, frequency, or phase, with the data signal, "piggybacking" the data on the carrier. Multiple modulated carriers at different frequencies are sent through the transmission medium, such as a cable or optical fiber.