#5**+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}$$

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

heureka
May 15, 2015

#1**+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

gibsonj338
May 15, 2015

#3**+10 **

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

.

Alan
May 15, 2015

#4**+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

Melody
May 15, 2015

#5**+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