convert binary number 1010.1011 into decimal number since there is binary point here with frictional part
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Answer:
How do I convert the binary number 1010.1011 (yes, that’s a binary point) to decimal?
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Nick Picard
Answered 2 years ago
How do I convert the binary number 1010.1011 (yes, that’s a binary point) to decimal?
Just a quick note: when you’re working in something other than base 10, it’s not a “decimal” point (that’s reserved for the decimal, or base 10 system). The general term is “radix point.” I love that word. (Edit: the original answer referred to the point as a “decimal point.”)
To answer your question, let’s review what the different slots in binary mean. The first slot to the left of the radix point represents 20 , the next represents 21 , and so on. So the left half of your number is
10102
=23+21
=1010
The first slot to the right of the radix point represents 2−1 . Extrapolating, the left half looks like this:
.10112
=2−1+2−3+2−4
=.5+.125+.0625
=.687510
Hopefully you are now equipped to put it all together.
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Emily Moon
Updated 3 years ago
How do you convert decimal numbers to binary?
Before we convert a decimal number into binary let’s make sure we understand how regular decimal numbers work. We can use the decimal number 1337 as a random number to work through an example.
When we write the decimal number 1337 we are actually using a form of shorthand. What we really mean when we say 1337 is 1×1000+3×100+3×10+7×1
In words, “1337 is 1 thousands, 3 hundreds, 3 tens, and 7 ones”. But notice that thousands, hundreds, tens, and ones, are just powers of 10.
So 1337=1×103+3×102+3×101+7×100
If we weren’t already so used to decimal numbers and we wanted to ‘build’ this decimal number from scratch, we could ask ourselves, “how many 103 s will take to build that number? How many 102 s ?” And so on.
Now let’s m
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Vaclav Krpec
Answered 1 year ago
What is the method of converting a 1011101101 decimal to a binary number?
A very simple recursive algorithm (for non-negative integers) goes like this:
Let N be your function argument, D a local variable (binary digit)
If N is odd, set D to ‘1’ and decrement N
Otherwise, set D to ‘0’
Set N to N/2 (note that N is definitely even before the division)
If N is non-zero, call this very function recursively
Push D to output
As you can see, at each call of this function, one binary digit is produced. They are calculated from least significant to most significant and the recursion makes sure that they are printed in the correct, natural order to the output (i.e. most significant first). That’s, in fact, the only reason for the recursive approach; if you don’t mind to get the digits in reverse (least significant first), you can use a simple loop (printing/storing the digit before the loop condition).
Note that I won’t include a proof that the above really works. Analyse the algorithm and realise why it does yourself. That way, you understand.
Also note that you don’t need to do it like this if you work with numbers using a computer—as computers already store data in binary. Should you like to print a number in binary, you can use much faster algorithm which uses right bit shift instead of division and bitwise AND for checking parity & setting D—I’ll leave that to you to ponder upon; by realising how does that work yourself, you’ll comprehend better than if I just showed you.