Next: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates Contents
Using NAND gatesNOTFigure 12.10: Realizing a NOT gate using a NAND gate
OR The following statements are called DeMorgan's Theorems and can be easily verified and extended for more than two variables.
(12.1)(12.2)
(12.3)(12.4)In general: (12.5)Thus :(12.6)
Now it is easy to see that , which can be checked from the truth table easily. The resulting realization of OR gate is shown in 12.11
Figure 12.11: Realization of OR gate by NAND gates
AND gateFigure 12.12: Realization of AND gate by NAND gates
X-OR gate
(12.7)
Clearly, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates.
Figure 12.13: X-OR gate
X-NOR gate
(12.8)
Again, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates, i.e., NAND or NOR gates.
Figure 12.14: X-NOR gate
Next: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates Contentsynsingh 2007-07-25
The XOR operation can be implemented using only NAND gates by combining multiple NAND gates in a specific arrangement to achieve the desired XOR functionality.
Seven gates, they are: not, and, or, nor, nand, xor, xnor.
A&B = ((A&B)')' So two, it would go a - | ==NAND--=NAND-- b - | By using two NAND gates back-to-back, you can create a normal AND gate.
Next: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates ContentsUsing NAND gatesNOTFigure 12.10: Realizing a NOT gate using a NAND gateOR The following statements are called DeMorgan's Theorems and can be easily verified and extended for more than two variables.(12.1)(12.2)(12.3)(12.4)In general: (12.5)Thus :(12.6)Now it is easy to see that , which can be checked from the truth table easily. The resulting realization of OR gate is shown in 12.11Figure 12.11: Realization of OR gate by NAND gatesAND gateFigure 12.12: Realization of AND gate by NAND gatesX-OR gate(12.7)Clearly, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates.Figure 12.13: X-OR gateX-NOR gate(12.8)Again, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates, i.e., NAND or NOR gates.Figure 12.14: X-NOR gateNext: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates Contentsynsingh 2007-07-25
That title of "Universal Gate" is reserved for NAND gates because you can build all possible logic using only NAND logic . You can build even other basic logic like AND, OR and NOT using NAND.
two nand gates
A universal gate is a logic gate that can be used to implement any logic function. The NAND gate and NOR gate are examples of universal gates because any other logic gate can be constructed using only NAND or only NOR gates.
by multiplying two NAND gates
You cannot design a full adder using only OR gates. You also need AND gates. Typically, this can be done with just NAND gates.
universal gates are the ones from which we can design other gates also. for eg. NAND and NOR gates. they help in forming the uniformity in the circuits.
Final answer will be NAND bz from first NAND ans NOT AND then Again NOT ( NOT AND) ans AND then Again NOT ( AND) so final ans will be NAND.
There is no such thing as an R-S NAND gate.The datasheet for a 7474 IC will give you a schematic for a D flipflop using NAND gates only.