Question

It's a question based on the Binary system.

It's an easy question, I just don't understand some mathematical terms in the question.

http://screencast.com/t/H3K17LHwp0IE

Answer 1

the wording is indeed bizarre

Answer 2

but the procedure is straight forward, correct? you have successive powers of 2, and for 49 \(2^5=32\) is the largest power of 2 than is less than 49, so there is a 1 in the \(2^5\) place
then \(49-32=19\) and \(2^4=16\) is the next largest power of two that is less than 19, therefore there is a 1 in the \(2^4\) place
etc

Answer 3

Convert 49 to binary:
The largest power of 2 that fits in 49 is 32 = 2^5. So put a 1 in that column.
49-32=17.
The largest power of 2 that fits in 17 is 16=2^4. So put a 1 in that column.
17-16=1.
The largest power of 2 that fits in 1 is 2^0=1. So put a 1 in that column.

All the other columns remain 0.

Answer 4

it would be better if i knew how to subtract!!

Answer 5

Just keep trying! :D

Answer 6

So can you explain to me what this means? http://screencast.com/t/U2LeOeCyf

Answer 7

Just like \(1234 = 1000+2\cdot100+3\cdot10+4=1 \cdot 10^3 + 2 \cdot 10^2+3 \cdot 10^1+4 \cdot10^0\), in decimal.
We usually are not aware of all these powers of 10, we just remember the 1, 2 3 and 4 and their position.

It is the same with 49 in binary: it is \(1 \cdot 2^5+^1 \cdot 2^4+0 \cdot 2^3+ 0 \cdot2^2+0 \cdot2^1+1 \cdot2^0\).

If we forget about the powers of 2, we get: 110001. We just have to remember the 1, 1, 0, 0, 0 and 1 and their positions!

Answer 8

The weight of a digit depends on the position.
In 1234 (decimal), the weight of the 2 is 100, that of 3 is 10.

Answer 9

"And put 1s in the columns that sum to the decimal number" how a column will sum to the decimal number? FOR EXAMPLE THIS http://screencast.com/t/d3sOShvTx2

Which is the number that SUMS to which number? If I understand that I will get it

Answer 10

@ZeHanz

Answer 11

1234 is the sum of 1*1000+2*100+3*10+4*1, so it is the sum of a number of powers of 10.

In the same way, 1234 could also be written as the sum of a number of powers of 2.
In fact is easier, because there is always 1 or 0 times a power of two, whereas with 1234 written in base 10, there is e.g. 2 times 10² necessary to get the 200-part of it.

Shall we try to write 1234 as a binary number?

All the powers of 2 have the following weight:

2048 1024 512 256 128 64 32 16 8 4 2 1
2^11 2^10 2^9 2^8 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

The number 1234 has 1024=2^10 as the largest power of 2 in it.
So in that column goes a 1.

1234-1024=210.

512 is too big, so a 0 in that column.
256 is too big, so a 0 in that column.
128 fits, so a 1 in that column.

210-128=82.
64 fits, so a 1 in that column.
82-64=18.
32 is too big, so a 0 in that column.
16 fits, so a 1 in that column.
18-16=2
8 and 4 do not fit, so 0's in these columns.
2 fits, so a 1 in that column.
2-2=0. Nothing more to do!
Put a 0 in the column of 1.

Now see if adding up works:

2048 1024 512 256 128 64 32 16 8 4 2 1
2^11 2^10 2^9 2^8 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
0 1 0 0 1 1 0 1 0 0 1 0

\(1 \cdot 2^{10}+1 \cdot 2^7 +1 \cdot 2^6 + 1 \cdot 2^4+ 1 \cdot 2^1\)=
\(1024+128+64+16+2=1234\). It works!

Answer 12

So \(1234_{decimal}=10011010010_{binary}\)

Answer 13

many many many thankssss!!!!! :) I got it!

Answer 14

YW!
Just practise with a few numbers, and you will never forget anymore.