Converting binary decimal to hex: explain book's example?

[defeated_soldier]

Hi, My book says,

(111110001.101110) (base 2) = (1F1.B8)(base 16)

How ?

should i choose 4 digits in pairs and then convert into decimal and look for hex equivalent ?

but they are not in pairs .

For example , 111110001.101110

its very difficult to make pairs as well because you see there are some unpaired digits


so, how do i convert this binary into hexadecimal ?
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[arthur ohlsten]

111110001. 10111

set off in sets of 4 from decimal point

1 1111 0001 . 1011 1
1=1
1111=b
0001=1
for decimals
1011= 11
1000=8


1f1.b 8
Arthur

 

[arthur ohlsten]

another way
111110001.10111 is 497.72875

divide number by 2 and record remainder
497
248......1
124.......0
62.........0
31.........0
15.........1
7...........1
3...........1
1............1
0............1

497=11111001

multiply decimal by 2 and record digit
.71875
1.4375
0.875
1.75
1.5
1.0

.71875=10111
=================================================
now do the same with 16
497
31.........1
1...........15 or f
0............1

497=1f1

.71875
11.5 or b.5
8.0

.71875=b8

Arthur