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Universal Logic : Mux to Logic gates conversion

Posted by Nityanand Dubey on January 7, 2010

We have seen the universal gates in out previous posts. The NAND and NOR are called the universalgates because they can create any of the logic gates.

There is an another concept called Universal Logic, Universal logic can also be used to create any ofthe logic gates.

MUX and Decoders are called Universal Logic

In this post, we will see haw a 2:1 MUX can be used to create different logic gates.

1. Designing an Inverter using 2:1 MUX.

To design an inverter using 2:1 mux, we have to use the input as the select line of the MUX and thezeroth select line would be tied with Logic 1 and First select line would be tired with Logic 0,Now when the select line (Input) goes to 1 the out put will be 0 ( inverted).

Image : MUX to inverter -

Digital Design Nityanand's Weblog https://neovlsi.wordpress.com/category/interview-questions/digital-design/

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(h ps://neovlsi.files.wordpress.com/2009/12/mux2inv.jpg)2:1 mux as an inverter

2. Designing an AND Gate using 2:1 MUX.

To design an AND using 2:1 mux, we need to tie the zeroth input to Logic 0 and the First input tothe one of the input of the AND Gate. The other input of AND gate would be connected with theselect line of the MUX.

Now, the out put of the MUX would be 1 only if the both of the inputs are 1 otherwise it would be0 for all conditions.

Image : MUX to AND Gate -

(h ps://neovlsi.files.wordpress.com/2009/12/mux2and1.jpg)2:1 MUX as an AND gate

3. Designing an OR Gate using 2:1 MUX.

To design an OR using 2:1 mux, we need to tie the First input to Logic 1 and the Zeroth input tothe one of the input of the OR Gate. The other input of OR gate would be connected with the select lineof the MUX.

Now, the output of the MUX would be 1 when any oth the two inputs would be 1 otherwise itwould be 0 for all conditions.

Image : MUX to OR Gate -


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(h ps://neovlsi.files.wordpress.com/2009/12/mux2or.jpg)2:1 MUX as an OR Gate

4. Designing an NOR Gate using 2:1 MUX.

To design the NOR using 2:1 mux, we need to tie the Zeroth input of mux to one of the input of NORand another input of MUX is tied to 0 . The another input of NOR gate would be applied to the selectline of the MUX.

Now, the output of the MUX would be AB = (A+B). which is as same as the output of NOR Gate.

Image : MUX to NOR Gate -

(h ps://neovlsi.files.wordpress.com/2009/12/mux2nor.jpg)2:1 mux as a NOR Gate

5. Designing an NAND Gate using 2:1 MUX.

To design the NAND using 2:1 mux, we need to combine the AND Gate and inverter implementation

6. Designing an XOR Gate using 2:1 MUX.

To design the XOR using 2:1 mux, we need to tie the Zeroth input of mux to one of the input of XORand another input of MUX to the inverted of first input. The another input of XOR gate would beapplied to the select line of the MUX.

Now, the output of the MUX would be AB + AB which is as same as the output of XOR Gate.

Image : MUX to XOR Gate -


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(h ps://neovlsi.files.wordpress.com/2009/12/mux2xor.jpg)2:1 Mux as a XOR gate

7. Designing an XNOR Gate using 2:1 MUX.

To design the XNOR using 2:1 mux, we need to tie the First input of mux to one of the input of XORand another input of MUX to the inverted of first input. The another input of XOR gate would beapplied to the select line of the MUX.

Now, the output of the MUX would be AB + AB which is as same as the output of XNOR Gate.

Image : MUX to XNOR Gate -

(h ps://neovlsi.files.wordpress.com/2009/12/mux2xnor2.jpg)2:1 mux as a XNOR Gate

Posted in Digital Design | Tagged: 2:1 mux, 2:1 mux to, mus to NOR, mux to AND, MUX to inverter,mux to NAND, mux to OR, mux to XNOR, mux to XOR, universal logic | 29 Comments

What is a Universal Gate and Why NOR is called aUniversal gate?


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Posted by Nityanand Dubey on December 4, 2009

This is a continuation of previous post, in this post, we will see the NOR gate as a univarsal gate andcreate different gates using NOR gate.

As we know that NAND and NOR Gates are called Universal Gates since they can cerate any of theLogic Gate

Lets see to how to make all other logic gates by using the NOR Gate

1. NOR gate to NOT Gate conversion

Refer the following diagram

Digital : Image NOR to NOT

NOR to NOT Conversion

Here the same input is applied to the both inputs of a NOR Gate

According to NOR Gate If A and B are two inputs than output equation will be (A+B)

For this case :

= (X+X)= X= Inverted Input

2. NOR Gate to AND Gate Convertion

Refer following diagram for NOR to AND Gate conversion -

Digital : Image NOR to AND Conversion

NOR to AND Conversion

According to diagram


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s1 = (X+X) = Xs2 = (Y+Y) = Ys3= (s1+s2) = (X+Y)=> (X) .(Y)=> X.Y=> AND Gate

3. NOR Gate to OR Gate Convertion

Refer the following Diagram

Digital : Image NOR to OR Convertion

NOR to OR

For this case X and Y are the two inputs to a NOR gate and the output of the First NOR gate goesagain to an another NOR gates inputs.

=> s1 = (X+Y)=> s2 = (s1+s1) = s1=> s2 = ((X+Y))=> X+Y=> OR Gate

4. NOR Gate to NAND Gate Convertion


Digital : Image NOR to NAND

NOR to NAND Conversion



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s1 = (X+X) = Xs2 = (Y+Y) = Ys3 = (s1+s2) = (X+Y)=> (X) .(Y)=> X.Ys4 = (s3 + s3)=> s3=> (X.Y)=> NAND Gate

5. NOR to XOR Gate

Digital : Image NOR to XOR Gate Convertion

6. NOR to XNOR Gate

Digital : Image NOR to XNOR Gate Convertion

Posted in Digital Design | Tagged: Conversion, conversion of gates, NOR to AND, NOR to NAND,NOR to NOT, NOR to XNOR, NOR to XOR | 2 Comments

What is a Universal Gate and Why NAND is called aUniversal gate?

Posted by Nityanand Dubey on March 6, 2009

A Logic Gate which can infer any of the gate among Logic Gates. OR a gate which can be use to createany Logic gate is called Universal Gate

We have following Logic Gates

NOTANDORNANDNORXORXNOR

NAND and NOR Gates are called Universal Gates because all the other gates can be created by usingthese gates

In this post, we will see to how to make all other logic gates by using the NAND Gate

1. NAND gate to NOT Gate conversion


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Refer the following diagram

Digital : Image NAND to NOT

Nand to Not conversion

Here the same input is applied to the both inputs of a NAND Gate

According to NAND Gate If A and B are two inputs than output equation will be (A.B)

For this case :

= (X.X)= X

2. NAND Gate to AND Gate Convertion

Refer following diagram for NAND to and Gate conversion -

Digital : Image NAND to AND

NAND to AND conversion

For this case x and y are the two inputs to a NAND gate and the output of the First NAND gate goesagain to an another NAND gates inputs.

=> s1 = (X.Y)=> s2 = (s1.s1) = s1=> s2 = ((X.Y))=> X.Y

3. NAND Gate to OR Gate Conversion


Digital : Image NAND to OR


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NAND to OR Conversion


s1 = (X.X) = Xs2 = (Y.Y) = Ys3= (s1.s2) = (X.Y)=> (X) + (Y)=> X+Y

4. NAND Gate to NOR Gate Convertion


Digital : Image NAND to NOR

NAND to NOR conversion


s1 = (X.X) = Xs2 = (Y.Y) = Ys3= (s1.s2) = (X.Y)=> (X) + (Y)=> X+Ys4 = (s3.s3) = s3=> (X + Y)

5. NAND to XOR Gate

Digital : Image 5

6. NAND to XNOR Gate

Digital : Image 6


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Posted in Digital Design | Tagged: AND, conversion of gates, Logic Gates, NAND, NAND to AND,NAND to NOT, NAND to OR, NOR, NOT, OR, XNOR, XOR | Leave a Comment

What is the difference between a Latch and a Flip-Flop

Posted by Nityanand Dubey on August 21, 2008

The Latches and Flop-flop, both are considered as a sequential element of Digital Design. It means theoutput of both blocks; depend on the input as well as the previous output.

Here are some difference between the latches and Flip-flops(FF)

1. Functionality : The Latches are level sensitive blocks, it means the output may change any timeduring the active phase of clock ( As input changes) In other hand the Flip-flops as edge sensitive andoutput changes only with the clock edge. In between it does not changes (even though input toggles)

2. Area : The latches take less area than Flip-flops, Since the Flip-flops made of latches. The D Flip flopmade of two latches in master-slave configuration.

3. Speed: The latches are more faster than then the Flop flops, Since less number of gates used in thelatches,

4. . Clock : Latches may of may not have clocks. But A Flip-flop must be having a clock.

Posted in Digital Design | Tagged: difference between, FF, Flip-flop, latch, latch and Flip flop | 1Comment

Design an Inverter and a Pass Gate ( Buffer) using theXOR gate

Posted by Nityanand Dubey on July 27, 2008

The X-OR gate can be used as a Pass Gate and as an inverter. As per characteristic of an Inverter, theoutput should have opposite value of the inputLets look into the given figureDigital : Image XOR as Inverter


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(h ps://neovlsi.files.wordpress.com/2008/07/xorasinv.jpg)

From the given Image -

One of the inputs of XOR gate is tied with Logic Value 1. Lets see whether it would works as an Inverteror not

From the output equation of the XOR Gate -

Y = AB + ABWhereA and B are two Inputs to the XOR Gate and Y is the Output

According to the diagram, One input is tied with Logic 1

=> Y = A.(1)+ A.1=> Y = 0 + A=> Y = A

Summary : If we tie one input of an XOR Gate with Logic value 1 then XOR works as an Inverter

The X-OR gate can also be used as a pass Gate or a buffer that means it can be used to transmit thesame input signal to the output.

Let look into the given figure

Digital : Image XOR as Pass Gate

(h ps://neovlsi.files.wordpress.com/2008/07/xoraspass.jpg)

From the given Image -


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One of the inputs of XOR gate is tied with Logic Value 0.From the output equation of the XOR Gate -

Y = AB + AB

WhereA and B are two Inputs to the XOR Gate and Y is the Output

According to the diagram, One input is tied with Logic 0

=> Y = A.(0)+ A.0=> Y = A + 0=> Y = A

Summary : If we tie one input of an XOR Gate with Logic value 0 then XOR works as a buffer thatmean whatever we give at the input, same would appear at the output

Posted in Digital Design | Tagged: buffer, inverter, inverter using xor, pass gate, using xor, xor asinverter | 1 Comment

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