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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
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What are the advantages of nand gate?
because it is an universal gate that control and repairs other gates.
Minimum number of nand gates required to form full and half adder?
Check this link http://www.dumpt.com/img/viewer.php?file=bd6b3mqsa66fhr6c76l1.bmp
What is the logic circuit for a full adder using only NAND gate?
by the procedure design a half subtractor design a logic ciruit to add two numbers with five bits each drawthe logic diagram of afull adder using using NAND gates only ?
How NAND gate works?
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.
How many 2-input and gates can replace n-input and gate Does that apply for nand gates as well?
for a two input gate to represent as an n-input gate excatly n-1 two input gates are required. this implies that for a two input OR gate to represent a four input OR gate exactly three two input OR gates are required let F is =a+b+c+d =(((a+b)+c)+d) =((a+b)+(c+d)) in both the above cases + is used three times so three two input OR gates make a four input OR gates. This discussion doesnot hold good for NAND gates an example can illlustrate the reson:- take F=(a.b.c.d)'=a'+b'+c'+d' --------------------------->(1) (this is obtained by a four input NAND gate) let us take this in the manner we did it for an OR gate and we will then verify the result. =((a.b)'(c.d)')' =((a'+b').(c'+d'))' =(a'+b')'+(c'+d')' =ab+cd <------------------------(2) (1)is not equal to (2) so we can say that a NAND gate cannot be replaced in the manner as OR gate is replaced
Define universal gate?
A logic circuit of any complexity can be realized by using only the three basic gates (NOT, AND, and OR Gates). There are two universal gates, the NAND Gate and the NOR gate. Each of those can also realize logic circuit single-handedly. The NAND and NOR gates are therefore called universal gates.
What is universal logic gate?
universal logic gate is a gate using which you can make all the logic gates there are two such gates NOR gate and NAND gate
Why NOR gate is called universal gate?
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.
How OR gates can be realized using NAND gates?
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
What is the definition of universal gate?
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.
How many NAND gates are required to obtain OR gate?
two nand gates
The OR gate can be converted to the NAND function by adding----gate to the input of the OR 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
What two gates can be combined to create a NAND gate?
an AND gate and a NOT gate
Minimum Number of NAND gates required to realize the function AB?
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.
How can you replace end gate or gate and not gate with a 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.
Why universal gate is called universal?
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.
How nand gate acts as a universal gate?
A universal gate is a gate which can implement any Boolean function without need touse any other gate type.The NAND and NOR gates are universal gates.In practice, this is advantageous since NAND and NOR gates are economical andeasier to fabricate and are the basic gates used in all IC digital logic families.In fact, an AND gate is typically implemented as a NAND gate followed by aninverter not the other way around!!Likewise, an OR gate is typically implemented as a NOR gate followed by an inverternot the other way around!!A universal gate is a gate which can implement any Boolean function without need touse any other gate type.The NAND and NOR gates are universal gates.In practice, this is advantageous since NAND and NOR gates are economical andeasier to fabricate and are the basic gates used in all IC digital logic families.In fact, an AND gate is typically implemented as a NAND gate followed by aninverter not the other way around!!Likewise, an OR gate is typically implemented as a NOR gate followed by an inverternot the other way around!!can be combined to produce AND, OR,NOT,XORand XNOR gates
