Consider a simple program that asks the user to supply an integer base value and a positive integer exponent. The program then displays the value of the base raised to the specified exponent. The variables are:
b represents the base
n represents the exponent
p represents bn
The graphic below illustrates just the processing logic; the input and output is not shown.
The variable, p, is given an initial value of 1. If n is initially zero, then the test fails immediately and p is still 1. This is correct because b0 = 1 for any nonzero b. If n is initially greater than zero, then the value of p is repeatedly multiplied by the base value, b. After each multiplication, the value of n is decreased by 1. Eventually, the loop terminates and p = bn.
The table below illustrates a sample run of this program where the user entered a value of 2 for the base and a value of 3 for the exponent.
| Action | b | n | p | Comment |
| 2 | 3 | ? | Initial values after input. | |
| Execute: p = 1 | 2 | 3 | 1 | Initialize the result. |
| Test: n > 0 | 2 | 3 | 1 | Test condition is true. |
| Execute: p = p * b | 2 | 3 | 2 | p*b = 1*2 = 2 |
| Execute: n = n - 1 | 2 | 2 | 2 | n-1 = 3-1 = 2 |
| Test: n > 0 | 2 | 2 | 2 | Test condition is true. |
| Execute: p = p * b | 2 | 2 | 4 | p*b = 2*2 = 4 |
| Execute: n = n - 1 | 2 | 1 | 4 | n-1 = 2-1 = 1 |
| Test: n > 0 | 2 | 1 | 4 | Test condition is true. |
| Execute: p = p * b | 2 | 1 | 8 | p*b = 4*2 = 8 |
| Execute: n = n - 1 | 2 | 0 | 8 | n-1 = 1-1 = 0 |
| Test: n > 0 | 2 | 0 | 8 | Test condition is false. |
When the test condition becomes false, the loop will terminate and the final value of the result, 8, will be displayed.
Note: the For Loop Example page contains a program that does the same thing another way.