A CPU has circuits that can work out that 2 + 3 is 5, and that 6 – 4 is 2.
Another one:
2 + 3 * 4
Recall that * is a splat. It means multiply.
+, -, and * are numeric operators. Here are numeric operators you'll use in this course:
+
Add, like 2 + 9
–
Subtract, like 2 – 9
*
Multiply, like 2 * 9
/
Divide, like 2 / 9
^
Raise to a power, like 3 ^ 3 (that's 27)
–
Unary minus, like -3 (that's negative 3)
2 + 3 * 4
… is a numeric expression. That is, a calculation that works out a number.
You might think that the expression…
2 + 3 * 4
…works out to 20. 2 + 3 is 5, and 5 * 4 is 20. But actually:
2 + 3 * 4 is 14
That's because the CPU doesn't use the operators from left to right. Instead, some operators have a higher precedence than others. The CPU does * before it does +. So it's 3 * 4 is 12, and 2 + 12 is 14.
If you wanted the CPU to do the + first, add parentheses:
(2 + 3) * 4 is 20
Here are the numeric operators again, in precedence order:
()
CPU does anything in parens first.
–
Unary minus, like -3 (that's negative 3)
^
Raise to a power, like 3 ^ 3
* and /
Multiply and divide have equal priority, done left to right.
+ and -
Add and subtract have equal priority, done left to right.
The operators in…
3 - 5 + 2 * 2 ^ 2 + 3
… would be done in this order…
3 - 5 + 2 * 2 ^ 2 + 3 becomes 3 - 5 + 2 * 4 + 3
3 - 5 + 2 * 4 + 3 becomes 3 - 5 + 8 + 3
3 - 5 + 8 + 3 becomes -2 + 8 + 3
-2 + 8 + 3 becomes 6 + 3
6 + 3 becomes 9
h1. Your turn
Work out each of the following.
Summary
The evaluator is part of the CPU. It can do arithmetic. It understands operators, like +, -, and *. Some operators have precedence over others. Use parens to change execution order.
