There are two forms of the NAND gate. Inverted input: Ouput = not Input1 and not Input2 and not Input3 ...
Inverted output: Output = not (Input1 and Input2 and Input3 ...)
Out= A'B'C+AB'C'+AC'A'+ABC
NAND gates are universal gates and can be used to construct any of the logic gates (AND, OR, NOT, NOR, XOR, XNOR). The easiest way to figure this out is to use basic Boolean Laws. For instance, to create a NOT gate (A'), tie one of the NAND gate's input to logic high: (A+1)' = A'. To create an AND gate (AxB), use two NANDs in series, with the second one configured as an inverter: (AxB) = ((AxB)')'
A+b=
An AND gate is a logic gate performing a Boolean logic AND operation.
The NAND gate has two or more inputs, and one output. This output is the complement of the AND of all the bits and will only be 0 if all the inputs are 1.A NOT gate on the other hand has only 1 input, and the output is the complement of this input.So to make a NAND gate into a NOT gate, we should tie (short, connect to same value) all the inputs of the NAND gate. At the output we would have the complement of the signal given at the tied inputs.This way we have a NOT gate from a NAND gate.
This is a term from digital electronis referring to a Negated AND or NOT AND gate. A NAND gate is a logic gate that produces an output which is false only if all its inputs are true. Boolean functions are activated by use of NAND gates.
(a'b+b'a)'
the not gate applied to and gate is nand gate
when the two inputs are shorted, a NAND gate acts like a NOT gate. hence AND = NAND + NOT For OR gate, inverse both the inputs before connecting them to a NAND gate. So three NAND gates would be needed.
Out= A'B'C+AB'C'+AC'A'+ABC
A nand gate can be made from an and gate by introducing an inverter at the output of the gate.
74ls00 is the ic no. Of nand gate
nand 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
For 2-input EX-OR gate, if one input is A, the other input is B, and the output is Y. Then the Boolean expression for EX-OR (XOR) function (gate) is Y=A⊕B The output Y is true if either input A or if input B is true, but not both.Y= ( (A and NOT B) or (NOT A and B) ) ;
NAND gates are universal gates and can be used to construct any of the logic gates (AND, OR, NOT, NOR, XOR, XNOR). The easiest way to figure this out is to use basic Boolean Laws. For instance, to create a NOT gate (A'), tie one of the NAND gate's input to logic high: (A+1)' = A'. To create an AND gate (AxB), use two NANDs in series, with the second one configured as an inverter: (AxB) = ((AxB)')'
Connect the two inputs of the NAND gate together.