
Steps:
 Get the last digit of the binary number, call this digit the currentDigit.
 Make a variable, let's call it power. Set the
value to 0.
 Multiply the current digit with (2^power),
store the result.
 Increment power by 1.
 Set the the currentDigit to the previous digit of the
binary number.
 Repeat step 3 until all digits have been multiplied.
 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 2^{0}
2^1 is equivalent to 2^{1}
2^2 is equivalent to 2^{2}
2^3 is equivalent to 2^{3}
2^4 is equivalent to 2^{4}
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 powerof2 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

