+0

# what is the binary representation of 2015?

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889
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what is the binary representation of 2015?

May 15, 2015

#5
+21848
+10

what is the binary representation of 2015 ?

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

$$2015_2~=~{1}~1~1~1~1~0~1~1~1~1~1$$

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May 15, 2015

#1
+1900
+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
+98168
+5

201510  = 111110111112

May 15, 2015
#3
+27547
+10

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

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May 15, 2015
#4
+99329
+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

May 15, 2015
#5
+21848
+10

what is the binary representation of 2015 ?

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

$$2015_2~=~{1}~1~1~1~1~0~1~1~1~1~1$$

heureka May 15, 2015
#6
+99329
+5

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