Converting base 10 to 2?

Question

Given the base ten number 95. Convert it to base two.

What's the work involved in this, have several similar questions.

Answer 1

First write down powers of 2 in descending order. Start with the biggest power of 2 less than or equal to your number:

64 32 16 8 4 2 1

You need a 64, so put a 1 under it and subtract from 95:
64 32 16 8 4 2 1
.1

95 - 64 = 31

Now you can't use 32 (too big) so put a 0 under it:
64 32 16 8 4 2 1
.1 . 0

You *can* use the 16 (smaller than 31), so put a 1 and subtract:
64 32 16 8 4 2 1
.1 . 0 . 1

31 - 16 = 15

Again you *can* use 8 (smaller than 15), so put a 1 and subtract:
64 32 16 8 4 2 1
.1 . 0 . 1. 1

15 - 8 = 7

You can use 4, then 2, then 1 also...
64 32 16 8 4 2 1
.1 . 0 . 1. 1 1 1 1

The final subtraction should leave 0:
7 - 4 = 3
3 - 2 = 1
1 - 1 = 0

64 32 16 8 4 2 1
.1 . 0 . 1 1 1 1 1

The number underneath (zeroes and ones) is your base 2 equivalent:
1011111 (base 2) = 95 (base 10)

To reverse the process, just put the powers of two *above* the number. Here it is easier if you write the powers of 2 starting from the *right*. Add the numbers that have a one underneath.

64 32 16 8 4 2 1
.1 . 0 . 1 1 1 1 1

1011111 (base 2) = 64 + 16 + 8 + 4 + 2 + 1 = 95 (base 10)

Answer 2

Try this.
In base 10 there are ten possible numbers:
0 1 2 3 4 5 6 7 8 9

In base 2 there are two possible numbers:
0 1

When looking at a base 2 number every number is a multiple of two.

Example: 10010
Position: 54321

Position value:
1 = 1
2 = 2
3 = 4
4 = 8
5 = 16
and so on...

So, base 2 (binary) 10010 = 16 + 2 = 18.
This is because the value in the 5th position for the right (16) is 1 and the value in the 2nd position from the right (2) is 1.

An easy way to look at this when converting from base 10 to base 2 is to see what multiple of 2 is the biggest number that is smaller than the number you are converting.

For example, 95.
The biggest multiple of 2 that is smaller than 95 is 64.

Since 64 is represented in base 2 as 1000000 we know this is where we can start.
Then, subtract 64 from 95 and we get 31.
The biggest multiple of 2 less than 31 is 16.
So then we get 1000000 + 0010000 = 1010000.
We then subtract 16 from 31 and get 15.

The biggest multiple of 2 smaller than 15 is 8.
8 is represented as 1000 in base 2.
We add 8 to our result: 1010000 + 1000 = 1011000

We keep finding the biggest multiple of two smaller than our remaining value until we get:
1011111 = 95
7654321
1234567
Position 7 = 64
Position 5 = 16
Position 4 = 8
Position 3 = 4
Position 2 = 2
Position 1 = 1

64 + 16 + 8 + 4+ 2 + 1 = 95

Hope this helps.

Answer 3

Think of it as 95 ones. That's 47 twos with 1 left over.
Divide by 2 and put down the remainder
47 1
Keep doing this till you get 1 for a quotient.
Here's the whole computation:
95
47 1
23 1 1
11 1 1 1
5 1 1 1 1
2 11 1 1 1
1 0 1 1 1 1 1.
The answer is 1 0 1 1 1 1 1.

Answer 4

Base two column values are 2^6, 2^5, 2^4, etc.

since 2^7 = 128 is greater than 95 you would start with 2^6=64 subtracted from 95 leaves 31. 2^4 = 16 subtracted from from 31 leaves 15. 2^3=8 subtracted from 15 leaves 7. 2^2=4 from 7 leaves 3 and 2^1 = 2 from 3 leaves 1. So we have 1011111 in base two.

Answer 5

The easiest algorithm is successively to divide the base ten value by 2 and list the remainders. When you're done, the remainder terms in reverse order give the base 2 value.

95÷2 = 47 with remainder 1
47÷2 = 23 with remainder 1
23÷2 = 11 with remainder 1
11÷2 = 5 with remainder 1
5÷2 = 2 with remainder 1
2÷2 = 1 with remainder 0
1÷2 = 0 with remainder 1

95_10 = 1011111_2

Answer 6

Write 95 as the sum of powers of 2.
95 = 64 + 16 + 8 + 4 + 2 + 1
= 2^6 + 0^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0

The powers tell you where 1s and 0s should go.
1011111

Answer 7

know everyone means to help, but check Wikipedia first when you have a straight forward question like this, okay?!
http://en.wikipedia.org/wiki/Logarithms
here is the website for Logarithms
basically, when you change bases you divide the log of the number you have in base 10 by the log of the "base" that you are converting to..... in this case
log 2 (95) = log (95) / log (2) = 6.5698
to check, raise 2 to this power 2^(6.5698) = 95
this formula works for any base you need to change to
log of 100 in base 3, log 3 (100) = log(100) / log (3) = 4.1918
check with 3 ^4.1918 = 100.
check the website
hang in there and be prepared

Answer 8

Headings for base 2 are shown:-

128__64__32__16__8__4__2__1
_____1___0___1___1__1__1__1

95 base 10 = 1 0 1 1 1 1 1 base 2

Answer 9

example log 10 (95) where 10 is the base and 95 is the number...change to base 2 using the change of base formula:

log 10 (95) = log 2 (95) / log 2 (10)

basically the log with new base of the number divided by the log with new base of the old base number

Check this site for more help if you need....

http://www.purplemath.com/modules/logrules4.htm

Answer 10

converting base 10 to base 2
95 to base 10= 1011111 to base 2

check this website link as to how i converted it

http://mathbits.com/mathbits/compsci/Introduction/frombase10.htm