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Many programming languages for robot control support unique forms of operators that work with numbers only and let you manipulate the individual bits that make up those numbers. These are called bitwise operators. The following list shows the common characters or names used for bitwise operators. Note that some languages (namely Visual Basic) do not distinguish between bitwise and relational (logical) operators.
OPERATOR SYMBOL
NAME
FUNCTION
Not or ~ And or & Or or | Xor or ^
Bitwise Not Bitwise And Bitwise Or Bitwise Xor Shift left Shift right
Reverses the bits in a number; 1s become 0s and vice versa Performs And on each bit in a number Performs Or on each bit in a number Performs Xor on each bit in a number Shifts the values of the bits 1 or more bits to the left Shifts the values of the bits 1 or more bits to the right
Let s use some bitwise operators in an example. Suppose you assign 9 to variable This and 14 to variable That. If you bitwise And (& symbol) the two together you get 8 as a result. Here are the binary equivalents of the values 9 and 15 (only four bits are shown since 9 and 14 can be expressed in just four bits):
DECIMAL NUMBER
BINARY EQUIVALENT
9 14
1001 1110
VARIABLES, EXPRESSIONS, AND OPERATORS 95
Using the And truth table given earlier, manually compute what happens when you bitwise And these two numbers together: 1001 1110 & ____ 1000 9 14 8
Using the same numbers for a bitwise Or computation, we get: 1001 1110 ____ 1111 9 14 15
Here s just one example of how this bitwise stuff is handy in robotics: bitwise And and bitwise Or are commonly used to control the output state of a robot s computer or microcontroller data port. The port typically has eight output pins, each of which can be connected to something, like a motor. Suppose the following four bits control the activation of four motors. When 0 the motor is off; when 1 the motor is on.
0000 0010 1100 all motors off second motor on fourth and third motor on
and so forth. Note that the rightmost bit is motor 1, and the leftmost is motor 4.
Suppose your program has already turned on motors 1 and 4 at some earlier time, and you want them to stay on. You also want to turn motor 3 on (motor 2 stays off). All you have to do is get the current value of the motor port:
1001 motors 1 and 4 on (decimal value equivalent is 9)
You then bitwise Or this result with
0100 motor 3 on (decimal value equivalent is 4)
Here s how the bitwise Or expression turns out: 1001 0100 ____ 1101 9 4 13
In this example, Or ing 9 and 4 happens to be the same as adding the decimal values of the numbers together. This is not always the case. For example, Or ing 1 and 1 results in 1, not 2.
96 PROGRAMMING CONCEPTS: THE FUNDAMENTALS
For your reference, the following table shows the binary equivalents of the first 16 binary digits (counting zero as the first digit and ending with 15). You can count higher by adding an extra 1 or 0 digit on the left. The extra digit increases the count by a power of two 31, 63, 127, 255, 511, 1023, and so on.
DECIMAL NUMBER
BINARY EQUIVALENT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
USING OPERATORS WITH STRINGS
Recall that a string is an assortment of text characters. You can t perform math calculations with text, but you can compare one string of text against another. The most common use of operations involving strings is to test if a string is equal, or not equal, to some other string, as in:
If "MyString" = "StringMy" Then
This results in False because the two strings are not the same. In a working program, you d no doubt construct the string comparison to work with variables, as in:
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