    CONVERTING BINARY TO DECIMAL Steps:
1. Get the last digit of the binary number, call this digit the currentDigit.
2. Make a variable, let's call it power.  Set the value to 0.
3. Multiply the current digit with (2^power), store the result.
4. Increment power by 1.
5. Set the the currentDigit to the previous digit of the binary number.
6. Repeat step 3 until all digits have been multiplied.
7. Sum the result of step 3 to get the answer number.

Example
Convert BINARY 11101 to DECIMAL

 NOTES MULTIPLICATION RESULT Start from the last digit of our example number (11101). Let's call this currentDigit. The value is 1. Multiply that digit with 2^0. Note that the power of 0 of any number is always 1. Note the ^ operator means to the power of. Ie: 2^0 is equivalent to 20 2^1 is equivalent to 21 2^2 is equivalent to 22 2^3 is equivalent to 23 2^4 is equivalent to 24 and so on. 1*(2^0) 1 Process the previous digit, which is 0, multiply that digit with the increasing power of 2 11101 (current digit is in bold) 0*(2^1) 0 Process the previous digit, which is 1, note that 2^2 means 2*2 11101 (current digit is in bold) 1*(2^2) 4 Process the previous digit, which is 1, note that 2^3 means 2*2*2 11101 (current digit is in bold) 1*(2^3) 8 Process the previous digit, which is 1, note that 2^4 means 2*2*2*2 11101 (current digit is in bold) 1*(2^4) 16 Here we stop because there's no more digit to process This number comes from the sum of the RESULTS column ANSWER 29

Basically, this is the same as saying:

1*(2^4) + 1*(2^3) + 1*(2^2) + 0*(2^1) + 1*(2^0)

or

1*(16) + 1*(8) + 1*(4) + 0*(2) + 1*(1)

The reason it's easier to start backward is because:

• Counting the number of digits takes extra time, and you might count wrongly.
• If you don't remember what a particular power-of-2 value, it's easy to calculate it from the previous value.  For instance, if you don't remember what the value of 2*2*2 is, then just double the value of 2*2 (which you already have - if you had started backward).

Another Example
Convert BINARY 1010 to DECIMAL

 MULTIPLICATION RESULT 0*(2^0) 0 1*(2^1) 2 0*(2^2) 0 1*(2^3) 8 ANSWER 10

Is constructing a table like above required?  No, it just depends on your preference.  Some people are visual, and the table might help.  Without a table, it's also easy.  If you want to be a speed counter, just remember that the value of the multiplier is always the double of the previous one.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...

 POWER OF 2s RESULT 2^0 1 2^1 = 2 2 2^2 = 2*2 4 2^3 = 2*2*2 8 2^4 = 2*2*2*2 16

Example
Convert BINARY 1010001 to DECIMAL.
Again, I'm starting backward here:

```(1*1) + (0*2) + (0*4) + (0*8) + (1*16) + (0*32) + (1*64) =
1   +   0   +   0   +   0   +   16   +   0    +   64   = 81
```  