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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
A NAND gate produces as output the inversion of the AND operation on it's inputs. So, since an AND gate only has high output when all inputs are high, a NAND gate will only have low output when all it's inputs are high. The NAND gate is particularly significant because NAND is a complete set in terms of logic operations, that is, with only NAND gates, you can simulate any logic function.
NAND gates are particularly useful in combinational logic circuits because simple AND-OR combinations can be simulated with an equal number of NAND gates alone.
A -> nand -> a'
b -> nand -> b'
a' b' -> nand -> a+b
The NAND gate's output is inverted with respect to the AND gate. NAND is short for "Not AND" or "Negated AND"
A NAND gate is an inverted (Negated) AND. It has a truth table as follows:
A B C
0 0 1
0 1 1
1 0 1
1 1 0
what are nand and nor gate
not
XORing X with 1 gives X', i.e., NOT(X). If we are able to construct a NAND (AND) using XOR, we can also obtain AND (NAND) from it, which makes XOR a universal gate since inverted inputs to a NAND (AND) will give OR (NOR). However XOR is not a universal gate! Therefore we cannot obtain NAND (AND) using XOR. :-) By, Tirtha Sarathi Ghosh Class 10 IIT Kanpur Aspirant
pass the inputs through an nand gate and again pass them through inverter,which is again formed by an nand gate
ans. 3 nand gates resoon :- OR GATE :- x+y NAND GATE :- x'+y' LOGIC :-so the logic is is we apply NAND to the inputs x' and y' instead of xand y we would get x+y DESIGN PROCEDURE 1. for inverting the input x and y can be done by NAND gates , 2. take a NAND gate and pass both x in both the inputs it means x NAND x gives you x' 3. follow similar procedure for inverting y 4. and then all the outputs of those NAND gates as the inputs of another NAND gate
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.
NAND gate
NOT Gate
When the two input terminals of a NAND gate are short circuited, it acts as a NOT gate.
A: NAND implies not and to be true both input must be hi or true <> There are two flavors of NAND gate. The positive input/negative output NAND will have a low output if and only if both inputs are high. The negative input/positive output NAND will have a high output if and only if both inputs are low.
That package contains four 2-input NAND gates with Schmitt-trigger inputs.
A 2 input NAND gate requires 4 NOR gates.A 3 input NAND gate requires 5 NOR gates.A 4 input NAND gate requires 6 NOR gates.etc.
I suppose so. If a three input NAND is used as a two input device, the third input can be viewed as an inhibit input. Also some NAND devices can be "3 stated" where the output goes to a high impedance.
A: It is simply a function of negating a true input, the other characteristics s that it is limited in fan-in fan -out capabilities
Connect both inputs of the NAND gate together to form a single input. Tie one input of the NAND gate to a logic high (Vcc) and connect the other input to the desired input signal.
All other logic gates can be made using XOR and XNOR, but to get NOT, you need to do (input) XOR 1 or (input) XNOR 0, but with NAND, you don't need 1: (input) NAND (input).
Short the inputs together. Logic: A High input, with the inputs shorted together, will be H+H at the input side of the NAND gate, therefore resulting in a low output. A Low input, with both inputs shorted together, is L+L for inputs, resulting in a High output. Also, a NOR gate can be used in exactly the same way.
XORing X with 1 gives X', i.e., NOT(X). If we are able to construct a NAND (AND) using XOR, we can also obtain AND (NAND) from it, which makes XOR a universal gate since inverted inputs to a NAND (AND) will give OR (NOR). However XOR is not a universal gate! Therefore we cannot obtain NAND (AND) using XOR. :-) By, Tirtha Sarathi Ghosh Class 10 IIT Kanpur Aspirant
yes (a or b)' = a' and b' a or b = (a' and b')' a or b = a' nand b'