Number System

Basic of Number System.

Number System

HELLO DOSTO !!

Today we will learn about a number system that computers can understand......

OBJECTIVES:-

♦ Digital Computers and Digital Systems

♦ Types of Number System

♦ Number-base Conversions

  1. Decimal to other

  2. other to Decimal

✪Digital Computers and Digital Systems

There are two types of signals:-

  1. analog signal

  2. Digital signal

✬Analog system

The signal may vary continuously over a specified region.

✬Digital system

  1. The physical quantities or signals can assume only discrete values.

  2. Greater accuracy

\=> Binary values

  • Digits 0 and 1

  • Words (symbols) False (F) and True (T)

  • Words (symbols) Low (L) and High (H)

  • And words On and Off

Block Diagram of Digital Computer

✬ Types of Number System

  1. Decimal Number

  2. Binary Number

  3. Octal Number

  4. Hexadecimal Number

  • Decimal Number: The system of numbers which has a base or radix is 10.....

    ex. (512.74)10

  • Binary Number: The system of numbers which has a base or radix is 2.....

    ex. (101.01)2

  • Octal Number: The system of numbers which has a base or radix is 8.....

    ex. (512.74)8

  • Hexadecimal Number: The system of numbers which has a base or radix is 16.....

    ex. (165.7A)16

✪ Number-base Conversions:-

  1. Decimal to other:

  2. Decimal to Binary:

    Let us understand with an Example...

    Q. (13.56)10

    Quotient Remainder | Value after Point:-

    13/2 = 6 1 | 0.56*2 = 1.12 1

    6/ 2 = 3 0 | 0.12*2 = 0.24 0

    3/2= 1 1 | 0.24*2 = 0.48 0

    1/2= 0 1 | Take two or Three values

ANSWER: (13.56)10=(1101.100)2

Decimal to octal

1. Convert (127)10 to Octal.

Solution: Divide 127 by 8

127 ÷ 8= 15(Quotient) and (7)Remainder

Divide 15 by 8 again.

15 ÷ 8 = 1(Quotient) and (7) Remainder

Divide 1 by 8, and we get;

1 ÷ 8 = 0(Quotient) and (1) Remainder

Hence, (127)10 = (177)8

✪ Decimal to Hexadecimal

Convert (960)10 into hexadecimal.

To convert decimal to hex, i.e. 960 base 10 to a hexadecimal number, follow the steps given below:

Step 1: First, divide 960 by 16.
960 ÷ 16 = 60 and remainder = 0

Step 2: Again, divide the quotient 60 by 16.
60 ÷ 16 = 3 and the remainder is 12.

Step 3: Again dividing 3 by 16, will leave quotient=0 and remainder = 3.

Step 4: Now taking the remainder in reverse order and substituting the equivalent hexadecimal value for them, we get,
3→3, 12→C and 0→0

Therefore, (960)10 = (3C0)16

  1. Other to Decimal:-

    Let us take an example

    to understand how we convert

    • Binary to Decimal :

Q. (1011)2 -> ()10

Answer: (1011)2 -> (11)10

HINT:- _ _ _

4 2 1

ANSWER: (101010011.110100)2=(523.64)8

  • Binary to Hexadecimal :

ngn

Table of number system represent in discreate system

Q. (11111011101110010)2 -> ()16

ANSWER: (11111011101110010)2 -> (1f8772)16

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