Third Chapter Lesson-2: Conversion of decimal number into binary, octal and decimal number.

At the end of this lesson-

  • 1. You will be able to convert a decimal number into binary number.
  • 2. You will be able to convert a decimal number into octal number.
  • 3. You will be able to convert a decimal number into hexadecimal number.

Number System Conversions

Decimal Number System to Other Base

  • Decimal Number System to Binary Number System
  • Decimal Number System to Octal Number System
  • Decimal Number System to Hexadecimal Number System

Other Base to Decimal Number System

  • Binary Number System to Decimal Number System
  • Octal Number System to Decimal Number System
  • Hexadecimal Number System to Decimal Number System

Conversion among Octal, Hexadecimal and Binary Number System

  • Octal & Hexadecimal to Binary Number system
  • Binary to Octal & Hexadecimal Number system

Conversion between Octal and Hexadecimal Number System

  • Octal to Hexadecimal Number system
  • Hexadecimal to Octal Number system

 

Decimal Number System to Other Base:

For Integer Part:

Step 1 − Divide the integer part of decimal number by the base of target number system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16)).

Step 2 − Get quotient and remainder from Step 1

Step 3 − Divide the quotient of Step 1 by the base of target number system

Step 4 − Get quotient and remainder from Step 3

Repeat this procedure until the quotient becomes zero.

Traverse the remainders from bottom to top to obtain the target number system.

 

For Fractional Part:

Step 1 − Multiply fractional part of the decimal number by the base of target number system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16)).

Step 2 −Write the integer part and fractional part of the product so obtained separately.

Step 3 − Multiply the fractional part of the previous product by the base of target number system.

Step 4 − Write the integer part and fractional part of the product so obtained separately.

Repeat this procedure until the fractional part remains 0.

[The fractional part does not terminates to 0 after several iterations.

So, let us find the value up to 4 decimal places.]

Traverse the real part column from top to bottom to obtain the target number system.

 

Decimal Number System to Binary Number System:

Example: Convert (17)10 to Binary number system.

So, (17)10  = (10001)2

Example: Convert (0.125)10 to Binary number system.

So, (0.125)10  = (.001)2

  • Convert (35.75)10 to Binary number system.
  • Convert (75.69)10 to Binary number system.

 

Decimal Number System to Octal Number System:

Example: Convert (423)10 to Octal number system.

So, (423)10 = (647)8

Example: Convert (.150)10 to Octal number system.

So, (.150)10 = (.11463…..)8

  • Convert (75.615)10 to Octal number system.
  • Convert (755.150)10 to Octal number system.

Decimal Number System to Hexadecimal Number System:

Example: Convert (423)10 to Hexadecimal number system.

So,  (423)10 = (1A7)16

Example: Convert (.150)10 to Hexadecimal number system. 

So, (.150)10 = (.266…..)16  

  • Convert (615.625)10 to Hexadecimal number system. 
  • Convert (125.150)10 to Hexadecimal number system. 

 

Lesson Evaluation-

Knowledge Based Questions:

Comprehension Based Questions:

Creative Questions:

Multiple Choice Questions:

 


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