A. When changing a number to base 10 you need to evaluate the following:
bn x a + ... + b x a' + a'' (a, a', a'' represent different digits and b represents the base)
B. Let's look at some examples:
Ex [1] 12415 =_________10.
a) To change this we need to put the number in this form:
53 x 1 + 52 x 2 + 5 x 4 + 1
b) This equates to 125 + 50 + 20 + 1 = 196.
c) The answer is 196.
Ex [2] 1223 = _________10.
a) To change this we need to put the number in this form:
32 x 1 + 3 x 2 + 2
b) This equates to 9 + 6 + 2 = 17.
c) The answer is 17.
C. Notice that the highest exponent is always 1 less than the number of digits. This might help in figuring out the answer faster.
Ex [1] 11011002 =_________10
a) Since there are 7 numbers we will start with 26.
b) Changing the form we get:
26 + 25 + 23 + 22 *Notice we can skip the 0's
c) This equates to 64 + 32 + 8 + 4 = 108. (These powers should be memorized from here).
d) The answer is 108.