Question

how to represent decimal integer 50 in binary

Answer 1

0b110010

Answer 2

If you think about how binary works, you can see that each spot has a value that is 2x the previous one. That is because it is base 2 and the max value that a set of binary numbers can represent is \(2^x\) So 1 binary digit can represent 2 decimal numbers, 0 and 1. 2 can represent \(2^2=4\) or 00 for 0, 01 for 1, 10 for 2, and 11 for 3. I'll get back to why 2 and 4 are not in these answers in just a second.

Before that, I want you look at powers of 2 so that you will so you will have the basics of how many binary digits are needed to make up your decimal number.

\(
\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline
\; & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline
2^x= & 2 & 4 & 8 & 16 & 32 & 64 & 128 & 256 \\ \hline
\end{array}
\)

Now, I said that I would get back to that not 2 and not 4 in a second. Well, for numbers up to 64-1 in decimal, it will take 6 digits. Notice the -1.

The -1 is because the first number is 0. Remember how one binary digit does 0 or 1, so \(2^1-1=1\) is the maximum decimal number it can represent. \(2^2-1=3\) so 3 is the max decimal that 2 spots can represent.

Now that you know how many digits are needed it is time to look at what each digit means in standard left to right numeric order. That way you can see how they would add up. You may notice I am doing 0 to 7 for the positions. This, again, relates to powers of 2.

\(
\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline
\text{Position} & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 \\ \hline
0= & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
1= & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \hline
2= & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ \hline
4= & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ \hline
8= & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ \hline
16= & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ \hline
32= & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ \hline
64= & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
128= & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
50= & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ \hline
\end{array}
\)

50 is really being represented by 32+16+0+0+2+0

So how are these are powers of 2? Well, the 0th position, when active, is \(2^0=1\) The 5th position is \(2^5=32\). This means the above is also:

\(50 = 2^5+2^4+0+0+2^1+0\)

Answer 3

Place values: 32 16 8 4 2 1
32+16+2=40

110010

Answer 4

easy way: use calculator! in most calculators, you can do this! it is 00110010.....
i mean he only asked for the answer, not how to do it!

Answer 5

@InsertUserNameHere.. "i mean he only asked for the answer, not how to do it!"

Then they should not have asked on OpenStudy. This is a tutoring site where people leard how to do their work. It is not an answer site.

People that just hand out answers get warnings, suspensions, and eventually are kicked off the site completely.

Answer 6

@e.mccormick "People that just hand out answers get warnings, suspensions, and eventually are kicked off the site completely."
whoah calm down! someone from my friends told me this site is for answers for homework or projects! i didnt know this!

what i know from my school (this goes way back) is that you could just use a table....
hope this is enough to not get me banned :/

Answer 7

The point is that explaining the process is good. Just giving the answer is not. And if you can get them to do the work, it is best.

Answer 8

i can agree, but i did remember a really easy process:

because it has to be 8 bit, you add 2 00 in the start!
and sorry for my poor skills, this drawing thing needs a replacement, or atleast shift for strait line.....