CONVERSION BETWEEN DIFFERENT NUMBER SYSTEM

Conversion Decimal To Binary:

Steps:-

• Divide the Decimal Number by 2
• Get the remainder from step 1
• Divide the quotient of the previous  by 2
• Record the remainder from step 3.
• Repeat step 3 and 4 for getting remainder until the quotient become 1 or 0.
• write the quotient and remainder from last step to first step or from bottom to top.

Ex-  37 = (?)2

Sol:

2	37	R
2	18	1
2	9	0
2	4	1
2	2	0
	1	0

(100101)₂

Conversion Binary To Decimal:

Steps:-

• Determine the position value of each digit
• Multiply the postion value with by the corrosponding power of 2.
• and Sum is the equivalent value in Decimal.

Ex- (100101)₂

=1x2⁵ + 0x2⁴ + 0x2³ + 1x2² + 0x2¹ + 1 x 2⁰

=1x32 + 0x16 + 0x8 + 1x4 + 0x 2 + 1x 1

=32+0+0+4+1

= (37)₁₀

(1011111)₂=

= 1x2⁶ + 0x2⁵ + 1x2⁴ + 1x2³ + 1x2² + 1x2¹ + 1x2⁰

=1x64 + 0x32 + 1x16 + 1x8 + 1x4 + 1x2 + 1x1

= 64+0+16+8+4+2+1

= (95)₁₀

Conversion Decimal To Octal:

Steps:-

• Divide the Decimal Number by 8
• Get the remainder from step 1
• Divide the quotient of the previous  by 2
• Record the remainder from step 3.
• Repeat step 3 and 4 for getting remainder until the quotient become 0 to 7(mean 0,1,2,3,4,5,6,7).
• write the cosent and remainder from last step to first step or from bottom to top.

Ex-    

68)₁₀= (?)₈

8	68	R
8	8	4
	1	0

(104)₈

Conversion Octal To Decimal:

Steps:-

• Determine the position value of each digit
• Multiply the postion value with by the corrosponding power of 8.
• and Sum is the equivalent value in Decimal.

Ex- (174)₈

=1x8² + 7x8¹ + 4 x 8⁰

=1x64+7x8+4x1

=64+56+4

= (124)₁₀

Conversion Decimal To HexaDecimal
Steps:-

• Divide the Decimal Number by 16.
• Get the remainder from step 1.
• Divide the quotient of the previous  by 16.
• Record the remainder from step 3.
• Repeat step 3 and 4 for getting remainder until the quotient become 0 to15.
• write the quotient and remainder from last step to first step or from bottom to top.
• Here Some Changes when we write Numbers, We Use A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.

Ex-  (813)10=(?)16

Sol:

(813)₁₀= (?)16

16	813	R
16	50	13
	3	2

Here The Number Became 32-13 that mean (32D)16.

Conversion Decimal To HexaDecimal:

Steps:-

• Determine the position value of each digit.
• Here Some Changes when we write Numbers, We Use A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.
• Multiply the postion value with by the corrosponding power of 16.
• and Sum is the equivalent value in Decimal.

Ex- (3AF)₈

=3x16² + Ax16¹ + F x 16⁰
=3x16² + 10x16¹ + 15 x 16⁰

=3x256+10x16+15x1

=768+160+15

= (943)₁₀