Classification of Memory in computer

Classification of memory:

This section provides classification of memories. There are two main types of memories i.e. RAM and ROM. Following tree diagram shows the classification of Memory:

Classification of memory
Classification of memory

ROM (Read Only Memory):

First classification of memory is ROM. The data in this memory can only be read, no writing is allowed. It is used to store permanent programs. It is nonvolatile type of memory. The classification of ROM memory is as follows:

a)      Masked ROM: the program or data are permanently installed at the time of manufacturing as per requirement. The data can not be altered.

The process of permanent recording is expensive but economic for large quantities.

b)      PROM (Programmable Read Only Memory): The basic function is same as that of masked ROM. but in PROM, we have fuse links. Depending upon the bit pattern, fuse can be burnt or kept intact. This job is performed by PROM programmer.

To do this, it uses high current pulse between two lines. Because of high current, the fuse will get burnt; effectively making two lines open. Once a PROM is programmed we cannot change connections, only a facility provided over masked ROM is, user can load his program in it. The disadvantage is a chance of regrowing of fuse and changes the programmed data because of aging.

c)       EPROM (Erasable Programmable Read Only Memory): the EPROM is programmable by the user. It uses MOS circuitry to store data. They store 1’s and 0’s in form of charge. The information stored can be erased by exposing the memory to ultraviolet light which erases the data stored in all memory locations. For ultraviolet light a quartz window is provided which is covered during normal operation. Upon erasing it can be reprogrammed by using EPROM programmer. This type of memory is used in project developed and for experiment use. The advantage is it can be programmed erased and reprogrammed. The disadvantage is all the data get erased even if you want to change single data bit.

d)      EEPROM: EEPROM stands for electrically erasable programmable read only memory. This is similar to EPROM except that the erasing is done by electrical signals instead of ultraviolet light. The main advantage is the memory location can be selectively erased and reprogrammed. But the manufacturing process is complex and expensive so do not commonly used.

RAM (Random Access Memory):

Second classification of memory is RAM. The RAM is also called as read/write memory. The RAM is a volatile type of memory. It allows programmer to read or write data. If the user wants to check execution of any program, user feeds the program in RAM memory and executes it. The result of execution is then checked by either reading memory location contents or by register contents.

Following is the classification of RAM memory. It is available in two types:

a)      SRAM (Static RAM): SRAM consists of flip-flop; using either transistor or MOS. for each bit we require one flip-flop. Bit status will remain as it is; unless and until you perform next write operation or power supply is switched off.

  • Advantages of SRAM:

1)  Fast memory (less access time)

2)  Refreshing circuit is not required.

  • Disadvantages of SRAM:

1)      Low package density

2)      Costly

b)      DRAM (Dynamic RAM): In this type of memory a data is stored in form of charge in capacitors. When data is 1, the capacitor will be charged and if data is 0, the capacitor will not be charged. Because of capacitor leakage currents the data will not be hold by these cells. So the DRAMs require refreshing of memory cells. It is a process in which same data is read and written after a fixed interval.

  • Advantages of DRAM:

1)      High package density

2)      Low cost

  • Disadvantages of DRAM:

1)      Required refreshing circuit to maintain or refresh charge on capacitor, every after few milliseconds.




Tags: classification of computer memory, classification of memory in computer.

Causal and Noncausal System (Causality Property)

Hi friends, today we will learn What is Causal and non-causal system?. These two are very important system in control systems. These systems are distinguished from their input output relationship. Let us see these systems one by one.

A)     Causal systems:

Definition: A system is said to be causal system if its output depends on present and past inputs only and not on future inputs.

Examples: The output of casual system depends on present and past inputs, it means y(n) is a function of x(n), x(n-1), x(n-2), x(n-3)…etc. Some examples of causal systems are given below:

1)      y(n) = x(n) + x(n-2)

2)      y(n) = x(n-1) – x(n-3)

3)      y(n) = 7x(n-5)

Significance of causal systems:

Since causal system does not include future input samples; such system is practically realizable. That mean such system can be implemented practically. Generally all real time systems are causal systems; because in real time applications only present and past samples are present. Since future samples are not present; causal system is memory less system.

B)      Anti causal or non-causal system:

Definition: A system whose present response depends on future values of the inputs is called as a non-causal system.

Examples: In this case, output y(n) is function of x(n), x(n-1), x(n-2)…etc. as well as it is function of x(n+1), x(n+2), x(n+3), … etc. following are some examples of non-causal systems:

1)      Y(n) = x(n) + x(n+1)

2)      Y(n) = 7x(n+2)

3)      Y(n) = x(n) + 9x(n+5)

Significance of non-causal systems:

Since non-causal system contains future samples; a non-causal system is practically not realizable. That means in practical cases it is not possible to implement a non-causal system.

  • But if the signals are stored in the memory and at a later time they are used by a system then such signals are treated as advanced or future signal. Because such signals are already present, before the system has started its operation. In such cases it is possible to implement a non-causal system.
  • Some practical examples of non-causal systems are as follows:

1)      Population growth

2)      Weather forecasting

3)      Planning commission etc.

For continuous time (C.T.) system:

A C.T. system is said to be “causal” if it produces a response y(t) only after the application of excitation x(t). That means for a causal system the response does not begin before the application of the input x(t).

The other way of defining the causal system is as follows:

A system is said to be “causal” if its output depends on present and past values of the input and not on the future inputs. If the input is applied at t = tm then the output at t = tm y(tm) will be dependent only on the values of x(t) for t ≤ tm.

Condition for causality: y(tm) = f[x(t); t ≤ tm]

Causal systems are physically realizable systems. The non-causal systems do not satisfy above condition. Non-causal systems are not physically realizable.

Condition for causality in terms of impulse response h(t):

The relation between y(t) and x(t) is given by,

y(t) = x(t)*h(t)

Where * represents convolution and h(t) is the impulse response of the system. The condition for causality in terms of the impulse response is as follows:

Condition for causality: h(t) = 0 for t<0

This condition states that a linear time invariant (LTI) system is “causal” if its impulse response h(t) has a zero value for negative values of time.

Solved problems on causal and non-causal system:

Determine if the systems described by the following equations are causal or non-causal.

1)      y(n) = x(n) + x(n-3)

Solution: the given system is causal because its output (y(n)) depends only on the present x(n) and past x(n-3) inputs.

2)      y(n) = x(-n+2)

Solution: this is non-causal system. This is because at n = -1 we get y(-1) = x[-(-1)+2] = x(3). Thus present output at n = -1, expects future input i.e. x(3)

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Linear or Non-linear Systems (Linearity Property)

Linear or Non-linear Systems (Linearity Property):

A linear system is a system which follows the superposition principle. Let us consider a system having its response as ‘T’, input as x(n) and it produces output y(n). This is shown in figure below:

Let us consider two inputs. Input x1(n) produces output y1(n) and input x2(n) produces output y2(n). Now consider two arbitrary constants a1 and a2. Then simply multiply these constants with input x1(n) and x2(n) respectively. Thus a1x1(n) produces output a1y1(n) and a2x2(n) produces output a2y2(n).

Theorem for linearity of the system:

A system is said to be linear if the combined response of a1x1(n) and a2x2(n) is equal to the addition of the individual responses.

That means,

T[a1 x1(n) + a2 x2(n)] = a1 T[x1(n)] + a2 T[x2(n)]…………….1)

The above theorem is also known as superposition theorem.

Important Characteristic:

Linear system has one important characteristic: If the input to the system is zero then it produces zero output. If the given system produces some output (non-zero) at zero input then the system is said to be Non-linear system. If this condition is satisfied then apply the superposition theorem to determine whether the given system is linear or not?

For continuous time system:

Similar to the discrete time system a continuous time system is said to be linear if it follows the superposition theorem.

Let us consider two systems as follows:

y1(t) = f[x1(t)]

And y2(t) = f[x2(t)]

Here y1(t) and y2(t) are the responses of the system and x1(t) and x2(t) are the excitations. Then the system is said to be linear if it satisfies the following expression:

f[a1 x1(t) + a2 x2(t)] = a1 y1(t) + a2 y2(t)…………….1)

Where a1 and a2 are constants.

A system is said to be non-linear system if does not satisfies the above expression. Communication channels and filters are examples of linear systems.

How to determine whether the given system is Linear or not?

To determine whether the given system is Linear or not, we have to follow the following steps:

Step 1: Apply zero input and check the output. If the output is zero then the system is linear. If this step is satisfied then follow the remaining steps.

Step 2: Apply individual inputs to the system and determine corresponding outputs. Then add all outputs. Denote this addition by y’(n). This is the R.H.S. of the 1st equation.

Step 3: Combine all inputs. Apply it to the system and find out y”(n). This is L.H.S. of equation (1).

Step 4: if y’(n) = y”(n) then the system is linear otherwise it is non-linear system.

Solved problem:

Determine whether the following system is linear or not?

y(n) = n x(n)


Step 1: When input x(n) is zero then output is also zero. Here first step is satisfied so we will check remaining steps for linearity.

Step 2: Let us consider two inputs x1(n) and x2(n) be the two inputs which produces outputs y1(t) and y2(t) respectively. It is given as follows:


Now add these two output to get y’(n)

Therefore y’(n) = y1(n) + y2(n) = n x1(n) + n x2(n)

Therefore y’(n) = n [x1(n) + x2(n)]

Step 3: Now add x1(n) and x2(n) and apply this input to the system.

Therefore 2

We know that the function of system is to multiply input by ‘n’.

Here [x1(n) + x2(n)] acts as one input to the system. So the corresponding output is,

y”(n) = n [x1(n) + x2(n)]

Step 4: Compare y’(n) and y”(n).

Here y’(n) = y”(n). hence the given system is linear.

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Time Variant or Time Invariant Systems

Time Variant or Time Invariant Systems


A system is said to be Time Invariant if its input output characteristics do not change with time. Otherwise it is said to be Time Variant system.


As already mentioned time invariant systems are those systems whose input output characteristics do not change with time shifting. Let us consider x(n) be the input to the system which produces output y(n) as shown in figure below.

Now delay input by k samples, it means our new input will become x(n-k). Now apply this delayed input x(n-k) to the same system as shown in figure below.

Now if the output of this system also delayed by k samples (i.e. if output is equal to y(n-k)) then this system is said to be Time invariant (or shift invariant) system.

If we observe carefully, x(n) is the initial input to the system which gives output y(n), if we delayed input by k samples output is also delayed by same (k) samples. Thus we can say that input output characteristics of the system do not change with time. Hence it is Time invariant system.


A system is Time Invariant if and only if


Similarly a continuous time system is Time Invariant if and only if


Now let us discuss about How to determine that the given system is Time invariant or not?

To determine whether the given system is Time Invariant or Time Variant, we have to follow the following steps:

Step 1: Delay the input x(n) by k samples i.e. x(n-k). Denote the corresponding output by y(n,k).

That means x(n-k)  → y(n,k)

Step 2: In the given equation of system y(n) replace ‘n’ by ‘n-k’ throughout. Thus the output is y(n-k).

Step 3: If y(n,k) = y(n-k) then the system is time invariant (TIV) and if y(n,k) ≠ y(n-k) then system is time variant (TV).

Same steps are applicable for the continuous time systems.

Solved Problems:

1)      Determine whether the following system is time invariant or not.

y(n) = x(n) – x(n-2)


Step 1: Delay the input by ‘k’ samples and denote the output by y(n,k)

Therefore y(n,k) = x(n-k) – x(n-2-k)

Step 2: Replace ‘n’ by ‘n-k’ throughout the given equation.

Therefore y(n-k) = x(n-k) – x(n-k-2)

Step 3: Compare above two equations. Here y(n,k) = y(n-k). Thus the system is Time Invariant.

2)      Determine whether the following systems are time invariant or not?

y(n) = x(n) + n x(n-2)


Step 1: Delay the input by ‘k’ samples and denote the output by y(n,k)

Therefore y(n,k) = x(n-k) + n x(n-2)

Step 2: Replace ‘n’ by ‘n-k’ throughout the given equation.

Therefore y(n-k) = x(n-k) + (n-k) x(n-k-2)

Step 3: Compare above two equations. Here y(n,k) ≠ y(n-k). Thus the system is Time Variant.

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Static or dynamic systems

Static or dynamic systems

In the last article we have discussed about introduction to the systems and its properties or classification. Let us study these Properties one by one.

a)      Static systems:

Definition: It is a system in which output at any instant of time depends on input sample at the same time.


1)      y(n) = 9x(n)

In this example 9 is constant which multiplies input x(n). But output at nth instant that means y(n) depends on the input at the same (nth) time instant x(n). So this is static system.

2)      y(n) = x2(n) + 8x(n) + 17

Here also output at nth instant, y(n) depends on the input at nth instant. So this is static system.

Why static systems are memory less systems?


Observe the input output relations of static system. Output does not depend on delayed [x(n-k)] or advanced [x(n+k)] input signals. It only depends on present input (nth) input signal. If output depends upon delayed input signals then such signals should be stored in memory to calculate the output at nth instant. This is not required in static systems. Thus for static systems, memory is not required. Therefore static systems are memory less systems.

b)      Dynamic systems:

Definition: It is a system in which output at any instant of time depends on input sample at the same time as well as at other times.

Here other time means, other than the present time instant. It may be past time or future time. Note that if x(n) represents input signal at present instant then,

1)      x(n-k); that means delayed input signal is called as past signal.

2)      x(n+k); that means advanced input signal is called as future signal.

Thus in dynamic systems, output depends on present input as well as past or future inputs.


1)      y(n) = x(n) + 6x(n-2)

Here output at nth instant depends on input at nth instant, x(n) as well as (n-2)th instant x(n-2) is previous sample. So the system is dynamic.

2)      y(n) = 4x(n+7) + x(n)

Here x(n+7) indicates advanced version of input sample that means it is future sample therefore this is dynamic system.

Why dynamic system has a memory?


Observe input output relations of dynamic system. Since output depends on past or future input sample; we need a memory to store such samples. Thus dynamic system has a memory.

For continuous time (CT) systems:

A continuous time system is static or memoryless if its output depends upon the present input only.


Voltage drop across a resistor.

It is given by,

v(t) = i(t)*R

Here the voltage drop depends on the value of the current at that instant. So it is static system.

On the other hand a CT system is dynamic if output depends on present as well as past values.

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Properties of a system

Properties of a system



A system is a physical device (or an algorithm) which performs required operation on a discrete time signal.

A discrete time signal is represented as shown in figure below.

Discrete time system
Discrete time system
  • Here x(n) input discrete time signal applied to the system. It is also called as excitation.
  • The system operates on discrete time signal. This is called as procession of input signal, x(n).
  • Output of the system is denoted by y(n). It is also called as response of the system.


When input signal is passed through the system then it is represented by following notation:


Here T is called as transformation operation. Similarly for continuous time system:



A filter is good example of a system. A signal containing noise is applied to the input of the filter. This is an input signal to the system. The filter cancels or attenuates noise signal. This is the processing of the signal. A noise-free signal obtained at the output of the filter is called as response of the system.

Classification (or properties) of the system:

Properties of systems are with respect to input and output signal. For the simplicity we will assume that the system has single input and single output. But the same explanation is valid for system having multiple inputs and outputs. Important properties (or classification) of the systems are listed below:

Now based on the properties, the systems can be classified as follows:

Properties of system
Classification of system

We will see these different types (i.e. properties) of a system in upcoming posts. So stay connected.

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