The number given is 1100 to the base 2 (which is in the "binary" system).
We have to convert to base 10, which is the "decimal" system.
If you understand how the decimal system works, it is not difficult to understand
binary.
In the decimal system, the unit's place has a value of 10^0 or 1, the 10's place
has a value 10^1 or 10, 100's place has a value 10^2 or 100 and so on.
So to get the value of a number in the decimal system, you multiply the unit's
place by 1 (or 10^0), 10's place by 10 (or 10^1), 100's place by 10^2 etc.
e.g. the number 1234 is actually (starting from the rightmost, unit's place,
and moving left, one digit at a time)
4*10^0 = 4 *1 = 4 +
3*10^1 = 3 *10 = 30 +
2*10^2 = 2 * 100 = 200 +
1*10^3 = 1 * 1000 = 1000 = 1000 + 200 + 30 + 4 = 1234.
Similarly, in the binary system each element is called a "bit" - 1 or 0.
(Just as a digit in the decimal system can have only 10 possible values 0
to 9, a "bit" in binary can have only 2 possible values - 0 or 1.
It is in base 2 (instead of 10), which means the rightmost bit has a value
of 2^0, the next has a value of 2^1 = 2, the next has a value of 2^2 = 4 and
so on.
So to convert 1100, we do the multiplication as follows (starting from right,
and moving left, one bit at a time)
0*2^0 = 0*1 = 0 +
0*2^1 = 0*2 = 0 +
1*2^2 = 1*4 = 4 +
1*2^3 = 1*8 = 8 = 0 + 0 + 4 + 8 = 12.
The binary number 1100 (base 2) has a value of 
in base 10.
Hope this helps :) Let me know if it is not clear.
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