### Arithmetic of Computers

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### Lesson 5

#### Page 154

We have seen that numbers can be represented by adding together multiples of powers of a particular base number. For example, we can represent the number 54 as a sum of muliples of powers of 4:
3(42) + 1(41) + 2(40)  = 3(16) + 1(4) + 2(1)  = 48 + 4 + 2 = 54.
We also know the names for the parts of the expression that are in the parentheses, as shown below:
exponents 3 (42)  + 1 (41)  + 2 (40) base
In each of the terms written within parentheses, the number that is to be used as a factor (4 in this case) is called the base, and the number that tells how many times the base is to be used as a factor is called the exponent. This is all familiar.
The numbers outside the parentheses in the expression above have a special name, too. These multipliers are called coefficients. In our example here the coefficients are 3, 1 and 2.
3 (42)  + 1 (41)  + 2 (40) coefficients
In the expression 4(103) + 9(102) + 2(101) + 1(100) what is the coefficient of 101?