Binary Fraction conversion question

[tuannie]

Hey everyone,

Would someone please be kind enough to direct me to a good explainatory tutorial site or that can explain to me in how I would go about in answering this question.

I don't know where to begin or start.

What is the decimal value of the binary fraction 1010.1010?

Regards,
tuannie

[Salem]

> 1010.1010
Well to the left of the radix point, it's 1, 2, 4, 8 (2^0, 2^1, 2^2, 2^3 etc)
To the right, it's 1/2, 1/4, 1/8, 1/16 (2^-1, 2^-2, 2^-3, 2^-4 etc)

[tuannie]

> 1010.1010
Well to the left of the radix point, it's 1, 2, 4, 8 (2^0, 2^1, 2^2, 2^3 etc)
To the right, it's 1/2, 1/4, 1/8, 1/16 (2^-1, 2^-2, 2^-3, 2^-4 etc)

Can you please explain it to me in more details. I still don't get what you mean sorry. :sad:

[Salem]

Well it it was decimal, would you still have a problem with it?

It's the same deal, just use base-2 instead of base-10.

[tuannie]

Well it it was decimal, would you still have a problem with it?

It's the same deal, just use base-2 instead of base-10.

Can you provide me with another example working out so that I can use the example question and try get an understanding out of it and attempt on my quesion.

Thanks in advance....

[orko]

we do binary calculation on following manner:

0    1    0   .    1    0    1
            0*2^0           1*2^(-3)        0           1/8 (.125)
      1*2^1            0*2^(-2)             2           0
0*2^2            1*2^(-1)                   0            1/2 (.5)
----------------------------------------------------------------
                    (Adding all)               2.     625

read carefully, then read salem's posting..... i hope u ll get ur ans. :).... cheers!

[anupam_smart]

Hey everyone,

Would someone please be kind enough to direct me to a good explainatory tutorial site or that can explain to me in how I would go about in answering this question.

I don't know where to begin or start.

What is the decimal value of the binary fraction 1010.1010?

Regards,
tuannie

Hello tuannie, :)
Here is something what i tried to explain the conversion u asked for. :idea:

Ok,
:cool:
U asked for the conversion of binary to decimal, check it out:
Let’s say we have to convert –
1010.1010 The no. which u gave;
We solve this kind of problems into two parts as follows:
(<LHS> . <RHS>)

1. First take the left hand side no. of the radix point( . ) which is 1010
to convert it into its equivalent decimal the method is as follows:
1 0 1 0
1*(2^3)+0*(2^2)+1*(2^1)+0*(2^0)=10

i.e. >start from the right-most digit (0 here);
>move from right to left;
>multiply each digit with (2^(position of digit from right-1));
>The sum of all these(10 here) as shown above will give u the decimal equivalent of the
LHS part of radix.

2. Now the important & difficult one;
The Right hand part of radix of the given binary no.
This is 1010 again.Since right-most 0 is of no significance, this can be ommitted
out.
1 0 1

1*(2^-1)+0*(2^-2)+1*(2^-3)=.625 or

[1/(2^1)]+[0/(2^2)]+[1/(2^3)]=.625

Hope u understood this i.e
>we have to move from left to right now.
>multiply each digit with (2^-(position of the digit form radix on left))
or
Divide each digit with (2^position of the digit from radix on left)
>Sum up all these, as above(.625 here) to get the decimal equivalent of RHS part
of no.

The last step is simple:
Just put the two results obtained in step1. & step2. together with the radix ( . )
to get the required result
Here, it would be=10.625
Thus,
Binary equivalent of 1010.1010 is =10.625

Enjoy,
:cool: :cool:

[Bench]

Can you provide me with another example working out so that I can use the example question and try get an understanding out of it and attempt on my quesion.

Thanks in advance....

You should really pick up Salem's point about decimal - Just imagine you're going back to infant school maths, where you add numbers using columns:

[Thousands] [Hundreds] [Tens] [Units] . [Tenths] [Hundredths]

eg, the number 194.3 is:

One hundred + Nine tens + Four units + Three tenths

In decimal, we get our column headers by powers of the base number (decimal is base 10)

1 unit * 10^-2 = 0.01 (hundredths)
1 unit * 10^-1 = 0.1  (tenths)
1 unit * 10^0 = 1 (units)
1 unit * 10^1 = 10 (tens)
1 unit * 10^2 = 100 (hundreds)
1 unit * 10^3 = 1000 (thousands)

in Binary, the principle is exactly the same.. except binary is base 2.

1 unit * 2^-2 = 0.25 (quarters)
1 unit * 2^-1 = 0.5  (halves)
1 unit * 2^0 = 1 (units)
1 unit * 2^1 = 2 (twos)
1 unit * 2^2 = 4 (fours)
1 unit * 2^3 = 8 (eights)

So, for the number 1001.0110, we need a table like this

[8] [4] [2] [1] . [0.5] [0.25] [0.125] [.0625]
 1   0   0   1  .   0      1      1       0

So, back to infant school maths - here's our calculation

One eight + No fours + No twos + One unit = 9
+
No halves + One quarter + One eighth + No sixteenths = 0.375

result = 9.375

[anupam_smart]

Hello Bench,
You explained it in a great manner,i really appreciate it.
Thanks.