The method of conversion in between hexadecimal and decimal numbers are same as conversion between Octal and decimal numbers. I tried to make explanation as easy as possible. I provide 2 tables, one is for calculated powers of 16 and the other is for hexadecimal numbers equivalent in decimal numbers.
Key Questions:
- Conversion between decimal and hexadecimal numbers
- How to convert decimal fraction into hexadecimal fraction
- How to convert hexadecimal fraction into decimal fraction
164
|
163
|
162
|
161
|
160
|
16-1
|
16-2
|
65536
|
4096
|
256
|
16
|
1
|
0.0625
|
0.0039
|
Hexa-decimal
|
00
|
01
|
02
|
03
|
04
|
05
|
06
|
07
|
08
|
09
|
0A
|
0B
|
0C
|
0D
|
0E
|
0F
|
Decimal
|
00
|
01
|
02
|
03
|
04
|
05
|
06
|
07
|
08
|
09
|
10
|
11
|
12
|
13
|
14
|
15
|
Decimal to Hexadecimal Conversion:
As we see in decimal to binary conversion and decimal to octal conversion when converting From decimal to binary number system we use repeated division by 2 and if decimal to octal number system we use repeated division by 8. So this time we are working with hexadecimal numbers so the repeated division by 16 method is used. And if we have mantissa or fractional part then we use repeated multiplication by 16 method. Let's start with examples.
Example#01:4859)10= ?)16
4859/16 =303 remainder 11)10=B)16
303/16= 18 remainder 15)10=F)16
18/16=1 remainder 2)10=2)16
Look at the highlighted numbers 12FB)16
Answer 4859)10= 12FB)16
Example#02:23456.235)10= ?)16
Solve integer part using division by 16
23456/16=1466 remainder 0 =0)16
1466/16=91 remainder 10)10=A)16
91/16=5 reminder 11)10=B)16
Look at the highlighted numbers 5BA0)16
Mantissa will be calculated by using repeated multiplication by 16
0.235*16=3.76 (most significant digit)
0.76*16=12.16)10=C.12)16
0.16*16=2.56. (least significant digit)
0.235)10=0.3C2)16
Answer 23456.235)10= 5BA0.3C2)16
Example#03:1359.79)10= ?)16
For integer use repeated division by 16
1359/16 =84 remainder 15)10=F)16
84/16= 5 remainder 4
1359)10=54F)16
For mantissa use repeated multiplication by 16
0.79*16=12.64 = C.64)16
0.64*16=10.24 = A.24)16
0.79)16=0.CA)16
Answer 1359.79)10= 54F.CA)16
Hexadecimal to Decimal Conversion:
As we know when converting from any number system to decimal number system we use sum of weights method. Like for binary numbers the sum of weights are powers of 2. For octal numbers the sum of weights are power of 8. Similarly for hexadecimal numbers the sum of weights are powers of 16.
Example#01: 12FB)16= ?)10
12FB)16=(1*163)+(2*162)+(F*161)+(B*160)
=(1*4096)+(2*256)+(15*16)+(11*1)
=4096+512+240+11
=4859)10
Answer 12FB)16= 4859)10
Example#02: 5BA0.3C2)16= ?)10
5BA0.3C2)16=(5*163)+(B*162)+(A*161)+(0*160)
.(3*16-1)+(C*16-2)+(2*16-3)
=(5*4096)+(11*256)+(10*16)+(0*1)
.(3*0.0625)+(12*0.00390625)
neglect 16-3 which is too small.
=20480+5632+160.+0.1875+
0.046875
=23455.23)10
Answer 5BA0.3C2)16= 4859)10
Example#03: 54F.CA)16= ?)10
54F.CA)16= (5*162)+(4*161)+(F*160).(C*16-1)+
(A*16-2)
=(5*256)+(4*16)+(15*1).+(12*0.625)+
.(10*0.0039)
=1280+64+15.75+0.039
=1359.79)10
Answer 54F.CA)16= 1359.79)10
.jpg)
.jpg)
