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Base Conversion

Base Conversion


1. Decimal to Other Base System
2. Other Base system to Decimal


 Decimal to Other Base System :

Step - 1 : Divide the Decimal number (Base 10) to be converted by the values of New Base.
Step - 2 : Get the Remainder from the Step 1  and write it aside.
Step - 3 : Divide the Quotient of the Step 1 by the New Base again.
Step - 4 : Again obtain the Remainder from Step 3 and note it aside.

Repeat these steps, and get the Remainders until the Quotient becomes Zero.

Step - 5 : Arrange the obtained Remainders in the Reverse Order. 

KEY HIGHLIGHTS : 

The Remainder that is obtained Last is  MOST SIGNIFICANT DIGIT (M.S.D.)
And ,the Remainder that is obtained at the Step 1 is the LEAST SIGNIFICANT DIGIT. (L.S.D.)

Example : Convert 34₁₀ into Binary.
Sol : 

Step 

Operation

Quotient

Remainder

Step 1

34 / 2

17

0

Step 2

17 / 2

8

1

Step 3

8 / 2

4

0

Step 4

4 / 2

2

0

Step 5

2 / 2

1

0

Step 6

1 / 2

0

1


On arranging the Remainders in the Reverse Order, 
Decimal  number , 34₁₀ → (100010)₂.   

Example : Convert 79₁₀ into Octal.
Sol : 

Step 

Operation

Quotient

Remainder

Step 1

79 / 8

9

7

Step 2

9 / 8

1

1

Step 3

1 / 801

On arranging the Remainders in the Reverse Order, 
Decimal  number , 79₁₀ → (117)₈

Example : Convert 147₁₀ into Hexadecimal.
Sol : 

Step 

Operation

Quotient

Remainder

Step 1

147/16

9

3

Step 2

9/16 09

On arranging the Remainders in the Reverse Order, 
Decimal  number , 147₁₀ → (93)₁₆

Other Base System to Decimal

Step 1 : Multiply the powers of the numbers in an increasing order with their respective Bases from Right to Left.

Example : Convert (47)₈ to decimal.
Sol :

Steps 

Octal Number

Decimal Conversion

Step 1

(47)₈

((4 x 8¹) + (7 x 8⁰))₁₀

Step 2

(47)₈

(32 + 7)₁₀

Step 3

(47)₈

(39)₁₀


Required Conversion is :
                    (47)₈ → (39)₁₀

Other Base System to Non - Decimal

Step 1 : Convert Other Base to Decimal (Base 10)
Step 2 : Convert Decimal to New Base System

Example : Convert (23)₈ to Binary.
Sol : First convert the Octal into the Decimal.

Steps

Octal Number

Decimal Conversion

Step 1 

(23)₈

((2 x 8¹) + (3 x 8⁰))₁₀

Step 2

(23)₈

(16 + 3)₁₀

Step 3

(23)₈

(19)₁₀


Then, convert the Decimal into Binary

Steps

Operation

Quotient

Remainder

Step 1

19 / 2

9

1

Step 2

9 / 2

4

1

Step 3

4/ 2

2

0

Step 4

2 / 2

1

0

Step 5

1 / 2

0

1


Required Conversion is :
                 (23)₈ → (19)₁₀ → (10011)₂

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