### Signals and Systems

Signal is a function that represent the variation of a physical quantity with respect totime.

Signals is usually classified into two main types :

a. Analog Signal: is a signal which can take any value within the given limit.

### b. Digital Signal: is a signal which can only take a specific number of values.

Data in d igital system is composed of a discrete value that is called bit (0 or 1 ). Bitsare usually represented by electrical signals such as voltage and current. Information

in digital system are represented with groups of bits called binary codes .

Digital System deals with signals represented in digital form.

Analog System deals with signa ls that are represented in analog form.

Advantages of Digital Techniques

Digital systems are generally easier to design

Digital circuits are less affected by noise.

Information storage is easy.

Limitations of Digital Techniques

o Most physical quantities are analog in nature.

o Processing digitized signals takes time.

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### Number System

Many number systems are in use in digital technology such as Decimal System

Binary System

Octal System

Hexadecimal Systems

With a decimal system we have 10 different digits, which are 0, 1, 2, 3, 4, 5, 6, 7, 8,

and 9.

Ex: (6) 10, (25) 10, (100) 10

A binary system has only 2 different dig its 0 and 1 . So to deal with a binary number

system is quite easier than a decimal system. So we generally use the binary system

when we deal w ith the digital world.

Ex: (01011) 2, (110011) 2

The right most digit in a number system is called the ‘Least Significant Bit’ (LSB) and

the left most digit in a number system is called the ‘Most Significant Bit’ (MSB)

1 1 0 0 1 1

### In an octal number system there are 8 digits 0, 1, 2, 3, 4, 5, 6, and 7. Hence, any octal

number cannot have any digit greater than 7.Ex: (6) 8, (37) 8, (255) 8

Similarly, a hexadecimal number system has 16 digits 0 to 9 and the rest of the six

digits are specified by letter symbols as A, B, C, D, E, and F. Here A, B, C, D, E, and

F represent decimal 10, 11, 12, 13, 14, and 15 respectively.

Ex: (6) 16, (16A) 16, (9F) 16, (7E) 16

10, 8 and 2 : are called the base or radix and they are used to indicate the type of the

number system.

### As human we use decimal Number system. However, Computers only understand

zeros and ones , therefore Binary System is introduced.However, dealing with a long bina ry code is usually confusing and may lead to

erroneous result. Therefore, octal and hexadecimal systems are used to represent

long binary codes .

### MSB LSB

Conversion Between Number SystemsDecimal to Binary Conversion

To convert a number in decimal to a number in binary we have to divide the decimal

number by 2 repeatedly, until the quotient القسمممممممممممم ناتج ) of zero is obtained. Then the

column of the remainder is read in reverse order (from bottom to top) .

Ex) Convert (26) 10 into a binary number .

### Ex) Convert ( 75 )10 into a binary number .

Fractional ConversionSo far we have dealt with the conversion of integer numbers only. If the number

contains a fractional part, we have to deal with integer part as before then deal with

fraction as follow:

Ex: Convert (25.625) 10 into a binary number.

### Integer Part

Then , we deal with the Fractional PartEx) Convert ( 34.7 5)10 into a binary number .