We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
927
6
avatar

what is the binary representation of 2015?

 May 15, 2015

Best Answer 

 #5
avatar+22153 
+10

what is the binary representation of 2015 ?

$$\begin{array}{rcrr}
& & \rm{q o u t i e n t} & \rm{r e m a i n d e r} \\
2015 & : 2 = & 1007 & 1 \\
1007 & : 2 = & 503 & 1 \\
503 & : 2 = & 251 & 1 \\
251 & : 2 = & 125 & 1 \\
125 & : 2 = & 62 & 1 \\
62 & : 2 = & 31 & 0 \\
31 & : 2 = & 15 & 1 \\
15 & : 2 = & 7 & 1 \\
7 & : 2 = & 3 & 1 \\
3 & : 2 = & 1 & 1 \\
1 & : 2 = & 0 & \textcolor[rgb]{1,0,0}{1} \\
\end{array}$$

 

$$2015_2~=~\textcolor[rgb]{1,0,0}{1}~1~1~1~1~0~1~1~1~1~1$$

.
 May 15, 2015
 #1
avatar+1904 
+5

2015 in binary is 11111011111

 

I do not know of an easy way to explain why 2015 in binary is 11111011111; however, I found a video that can explain it way better than I can.  Here is the web address:  https://www.khanacademy.org/math/pre-algebra/applying-math-reasoning-topic/alternate-number-bases/v/number-systems-introduction

 May 15, 2015
 #2
avatar+100483 
+5

201510  = 111110111112

 

 May 15, 2015
 #3
avatar+27789 
+10

Here's a detailed breakdown of the steps needed to turn 2015 decimal into binary:

 binary 1

 binary 2

.

 May 15, 2015
 #4
avatar+100800 
+10

I am going to say the same as Alan and the video clip  LOL

1024 is the biggest power of 2 that goes into 2015, so I will start there 

 

2015

= 1024 with 991 remaining

=1024+512+479 remaining

=1024+512+256+223 remaining

=1024+512+256+128+95remaining

=1028+512+256+128+64+31remaining

=1028+512+256+128+64+16+15remaining

=1028+512+256+128+64+16+8+7remaining

=1028+512+256+128+64+16+8+4+3remaining

=1028+512+256+128+64+16+8+4+2+1

 

$$\\=2^{10}+2^9+2^8+2^7+2^6\qquad+2^4+2^3+2^2+2^1+2^0\\
=11111011111$$

 

Of course you could just use this converter

http://www.binaryhexconverter.com/decimal-to-binary-converter        

 May 15, 2015
 #5
avatar+22153 
+10
Best Answer

what is the binary representation of 2015 ?

$$\begin{array}{rcrr}
& & \rm{q o u t i e n t} & \rm{r e m a i n d e r} \\
2015 & : 2 = & 1007 & 1 \\
1007 & : 2 = & 503 & 1 \\
503 & : 2 = & 251 & 1 \\
251 & : 2 = & 125 & 1 \\
125 & : 2 = & 62 & 1 \\
62 & : 2 = & 31 & 0 \\
31 & : 2 = & 15 & 1 \\
15 & : 2 = & 7 & 1 \\
7 & : 2 = & 3 & 1 \\
3 & : 2 = & 1 & 1 \\
1 & : 2 = & 0 & \textcolor[rgb]{1,0,0}{1} \\
\end{array}$$

 

$$2015_2~=~\textcolor[rgb]{1,0,0}{1}~1~1~1~1~0~1~1~1~1~1$$

heureka May 15, 2015
 #6
avatar+100800 
+5

I would not have thought to do it your way Heureka but I really like your approach.

 

I have put this thread in the "Great answers to Learn from" sticky thread.     

 May 26, 2015

12 Online Users

avatar
avatar
avatar