How can I convert the BINARY number 100100111000111 to a BASE 10 number?

Question

I have to show my work of how I get this also.
Thanks!

Answer 1

From right to left, a binary numbers value is 1,2,4,8,16,32,64,128, etc you see the pattern. If there's a 0 then you don't add the value...if there's a 1 then you do.

So if your binary number is 00001001 then the number on the right is worth 1...the fourth from the right is worth 8 so this represents the number 9.

Got it?

Answer 2

Hi, remember : The position in any number system is always standing for a power of the base number. For example:

In the decimal system 35 means 3*10^1 + 5*10^0. It is called the decimal system because the latin word for 10 is decimal and 10 is the base of the system. We need the numbers 0....9 to express all values. Like 9*10^2 + 7*10^1 + 4*10^0 = 974

Now the binary system.

Here we have 2 as base, and we only have 0 and 1 as digits
(that``s the reason for the name "binary", meaning in latin two) So in order to express the decimal 35 in the binary system we have to do the following:
First look at this

2^0 = 1 2^7 = 128
2^1 = 2 2^8 = 256
2^2 = 4 2^9 = 512
2^3 = 8 2^10 = 1024
2^4 = 16 2^11 = 2048
2^5 = 32 2^12 = 4096
2^6 = 64 2^13 = 8192
2^14 = 16384
2^15 = 32768

In order to transform decimal 35 in to binary we have to check which highest power of 2 is in 35 decimal. It is obviously 2^5 = 32.
the remaining 3 to 35 in decimal n ow can be expressed as 2^1 + 2^0.

Therefore we have

1*2^5 + 0*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 1*2^0

This gives us the notation in a binary system for 35 decimal:

100011

The opposite way is similar: Your binary number is

10010011000111

which means

1*2^13 + 0*2^12 + 0*2^11 + 1*2^10 + 0*2^9 + 0*2^8 + 1*2^7 + 1*2^6 + 0*2^5 + 0*2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 1*2^0
= 8192 + 0 + 0 + 1024 + 0 + 0 + 128+ 64+ 0 + 0 + 0 +4+ 2+ 1
= 9415

Answer 3

1 0 0 1 0 0 1 1 1 0 0 0 1 1 1
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

you want to add the numbers that have a 1 on top of it so:
15+12+9+8+7+3+2+1=the answer is your binary to base 10 conversion

a detailed explaination is at
http://www.purplemath.com/modules/numbbase.htm


Just a tip: you want to write out the numbers from right to left instead of left to right.

Answer 4

a thanks to comprehend binary numbers is to position in writing them in additional effective type (remember: for base 10, more effective type potential multiplying the digit by technique of the suitable potential of 10. for example, 123 = 1x10^2 + 2x10^a million + 3x10^0). So, we've 1101 = a million*2^3 + a million*2^2 + 0*2^a million + a million^2^0 = 8+4+0+a million = 13 the option is slightly extra conceptually perplexing: commence by technique of looking the biggest potential of two that is going into sixty 9. the reply is sixty 4 = 2^6 Now take the version: sixty 9 - 2^6 = 5 Now, what is going into 5? 4 = 2^2 is going into 5, and 5 - 4 = a million. for sure, a million = 2^0. So, we've that sixty 9 = 2^6 + 2^2 + 2^0 ==>1000101

Answer 5

The both answers above are correct.
Here you an Example;
Example: convert binary 1101001 to decimal:
1 + 8 + 32 + 64 = 105
In more detail but see the number backwards; 1001011
1=1
0=2 But not used it 0
0=4
1=8 it is used it 1
0=16
1=32 it is used it 1
1=64 it used it 1

Answer 6

and so on + 0(2)^3 + 1(2)^2 + 1(2) ^1 + 1(2)^0
....... + 0 + 4 + 2 + 1


1 0 0 1 0 0 1 1 1 0 0 0 1 1 1
16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1

- 18887 = 16384 + 2048 + 256 + 128 + 64 + 4 + 2 +1

left most bit is sign bit (if 1 then - otherwise + )
if u see 0 ignore that value (do't add)

Answer 7

1+ 0* 2^1 + 0 * 2^2 + 1 * 2 ^ 3 + 0*2^4+0*2^5+1*2^6+1*2^7+1*2^8 +0+0+0+ 1*2^ 11 + 1*2^12 +1*2^13

Answer 8

Here's the psuedo code:

s = "100100111000111"
n = 0
for i = 1 to length(s)
cur = int(mid(s,length(s)-1,1))
n = n + 2^i
next

Every location represents 2 raised to a given power.

Answer 9

It isn't hard!!!

Click the link given below, read the section
entitled 'Binary Simplified' carefully, then add
them up.

If you are *told* the answer, how will you ever
figure it out for yourself next time?? :o)

HTH