Conversions of Number system

Convert decimal to binary number system...


For find a binary no. we divide a decimal no. by 2 while there quotient become zero and arrange there remainder last to first.

Multiply by 2	quotient	remainder
2	250
2	125	0
2	62	1
2	31	0
2	15	1
2	7	1
2	3	1
2	1	1
	0	1
		Ans.  11111010

Convert decimal to octal number system...

For find a octal no. we divide a decimal no. by 8 while there quotient become zero and arrange there 

remainder last to first. 

Multiply by 8	quotient	remainder
8	250
8	31	2
8	3	7
	0	3
		Ans.  372

Convert decimal to hexadecimal number system...

For find a hexadecimal no. we divide a decimal no. by 16 while there quotient become zero and arrange there remainder last to first. 

Multiply by 16	quotient	Remainder
16	250
16	15	A
	0	F
		Ans.  FA

Convert binary to decimal number system...


In this we multiply last to first digit by 2 because it is binary no.
Let take example->  11111010
ans.   = 0*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 1*2^4 + 1*2^4 + 1*2^5 + 1*2^6 + 1*2^7
         = 0 + 2 + 0 + 8 + 16 + 32 + 64 + 128
         = 250


Convert octal to decimal number system...


In this we multiply last to first digit by 8 because it is octal no.
e.g.=> 372
ans.  =  2*8^0 + 7*8^1 + 3*8^2
        =  0 + 56 + 192
        =  250


Convert hexadecimal to decimal number system...


In this we multiply last to first digit by 16 because it is hexadecimal no.
e.g.=>  FA
ans.  =  A*16^0 + F*16^1
        =  10 + 16*15
        =  250


Convert hexadecimal to binary number system...


e.g.=> FA                                   [ F= 1111 in binary , A= 1010 ]      
 ans.  =  1111   1010


Convert binary to hexadecimal number system...


e.g.=>  111110101010
 ans.  = 1111  1010  1010       Note :->[ we divide it into threef parts of 4 digit category]
         =  F        A        A        [ we know F= 1111, A= 1010 ]
         = FAA



Convert octal to binary number system...


e.g.=>  2567            Note :->[ we divide it into four parts of 3 digit category]
 ans.   =  010  101  110  111
          =  010101110111



Convert binary to octal number system...


e.g.=>  010101110111
 ans.   =  010  101  110  111      Note :->[ we divide it into four parts of 3 digit category]
          =  2      5      6      7
          =  2567



Convert hexadecimal to octal number system...


Step1=> convert hexadecimal to binary no. system.
Step2=> convert binary to octal no. system.

Convert octal to hexadecimal number system...

Step1=> convert octal to binary no. system.

Step2=> convert binary to octal no. system.