The binary numbering system has powers of 2 while the decimal numbering system has powers of 10. For example, the decimal value 548 is actually

(8 x 1) + (4 x 10) + (5 x 100)

or

(8 x 10^0) + (4 x 10^1) + (5 x 10^2)

As you might have noticed, the right most digit is in the ones place. The digit at the left of it is at the tens place and the digit at the left of that is at the hundreds place. As you can see the place it multiplied by 10 as we go left.

The binary system has something like that exactly except that the place is multiplied by 2. So the first place is the ones place, the second is the twos place the third is the fours place and so on.

Also, in the decimal numbering system, we can put the digits from 0-9 in any place. Unlike the decimal numbering system, we can only put either 0 or 1 in a place when we're using the binary numbering system.

Converting a value from decimal to binary:

We'll take the value 5 as an example. We first write the binary places until the place is > the value we're trying to convert.

8    4    2    1

then we remove that place — the place that's > the value we're trying to convert (in this case it's the 8). So we're left with

4    2    1

We then ask ourselves, how many 4s does 5 have? Obviously 1 and 1 is remaining. So we put 1 under the 4s place.

4    2   1
1

Now we have 1 left. Does the 1 has any 2s in it? Of course no. So we put 0 in the twos place.

4    2    1
1    0    

Lastly, the 1 has a single 1 in it so we put a 1 under the ones place. (that's a lot of ones :D )

4    2    1
1    0    1

so the decimal value 5 in binary is 101.

Converting from binary to decimal:

this one is relatively easy. We just multiply the 1 or the 0 in each place by this place and add them all.

4    2    1
1    0    1

so

(1 x 1) + (2 x 0) + (1 x 4) = 1 + 0 + 4 = 5

Hope that helps!

The binary numbering system has powers of 2 while the decimal numbering system has powers of 10. For example, the decimal value 548 is actually

(8 x 1) + (4 x 10) + (5 x 100)

or

(8 x 10^0) + (4 x 10^1) + (5 x 10^2)

As you might have noticed, the right most digit is in the ones place. The digit at the left of it is at the tens place and the digit at the left of that is at the hundreds place. As you can see the place it multiplied by 10 as we go left.

The binary system has something like that exactly except that the place is multiplied by 2. So the first place is the ones place, the second is the twos place the third is the fours place and so on.

Also, in the decimal numbering system, we can put a digit from 0 through 9 in any place. We can only put either 0 or 1 in a place when we're using the binary numbering system however.

Converting a value from decimal to binary:

We'll take the value 5 as an example for the sake of simplicity. We first write the binary places until the place is > the value we're trying to convert

8    4    2    1

then we remove that place — the place that's > the value we're trying to convert (in this case it's the 8). So we're left with

4    2    1

We then ask ourselves, how many 4s does 5 have? Obviously 1. So we put 1 under the 4s place.

4    2   1
1

Now we have 1 left (because we took 4 from 5 and 5 - 4 = 1). Now does the 1 has any 2s in it? Of course not. So we put 0 in the twos place.

4    2    1
1    0    

Lastly, the 1 has a single 1 in it so we put a 1 under the ones place. (that's a lot of ones :D )

4    2    1
1    0    1

so the decimal value 5 in binary is 101.

Converting from binary to decimal:

this one is relatively easy. We just multiply the 1 or the 0 in each place by this place and add them all.

4    2    1
1    0    1

so

(1 x 1) + (2 x 0) + (1 x 4) = 1 + 0 + 4 = 5

Hope that helps!