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to ensure the calculation would be performed correctly. 13.1.4.3 Using Bitwise Operators Bitwise mathematical operations can be somewhat confusing to new robot programmers primarily because they are not taught in introductory programming courses or explained in introductory programming texts. This is unfortunate because understanding how to manipulate bits in the programming language is critical for robotics programming. Some languages simplify the task of accessing bits by the use of a single bit data type, while others do not provide you with any data types smaller than a byte (eight bits). The reason why manipulating bits in robots is so important is due to the organization of control bits in the controlling computer systems. Each I/O port register variable address will consist of eight bits, with each bit being effectively a different numeric value (listed in Table 13-4). To look at the contents of an individual bit, you will have to isolate it from all the others using the bitwise AND operator:
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Bit4 = Register & 16 ' Isolate Bit 4 from the rest of register s bits
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Looking at this for the first time, it doesn t make a lot of sense although when you consult with Table 13-4, by looking at the binary value you can see that the value of 16 just has one bit of the byte set to 1 and when this is ANDed with the contents of the register, just this one bit s value will be accurate all the others will be zero. The set bit value that isolates the single bit of the byte is known as a mask. You can either keep a table of mask values in your pocket at all times, or you can use the arithmetic value at the right of Table 13-4. The shift left (<<) operation of one bit is equivalent to finding the set power of 2 or using one of the binary, hex, or decimal values in the table you just don t have to do any thinking to use it. To show how the arithmetic value is used to facilitate writing a 1 in a bit of a register, you could use the assignment statement and expression:
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Register = (Register & ($FF ^ (1 << Bit))) | (1 << Bit)
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The expression first calculates the byte value with Bit set and then XORs it with all bits set to produce a mask, which will allow the value of each bit of the register to pass unchanged except for Bit, which becomes zero. The register value with Bit zero is then ORed with the
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TABLE 13-4 BIT NUMBER 0 1 2 3 4 5 6 7
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Different Bits in a Byte and Their Numeric Values BINARY VALUE %00000001 %00000010 %00000100 %00001000 %00010000 %00100000 %01000000 %10000000 HEX VALUE $01 $02 $04 $08 $10 $20 $40 $80 DECIMAL VALUE 1 2 4 8 16 32 64 128 ARITHMETIC VALUE 20 = 1 << 0 21 = 1 << 1 22 = 1 << 2 23 = 1 << 3 24 = 1 << 4 25 = 1 << 5 26 = 1 << 6 27 = 1 << 7
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bit set and the resulting value is stored in Register. The parentheses, while seemingly complex, force the expression to execute as desired.
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13.1.5 ARRAYS AND CHARACTER STRINGS
A variable is normally assigned to a specific memory location within the computer that cannot change. For many kinds of data, this is acceptable, but there will be cases when you would like to access a data address arithmetically rather than having a fixed address. The array variable modifier provides you with a number of different variables or elements, all based on a location in memory and given the same name, but accessed by their address within the variable. Fig. 13-3 shows how memory is used to implement an array of bytes. The actual byte (or array element) is selected by adding an index to the variable name. Normally the index is added to the address of the variable name, so the first index is zero. To read the third byte in the example array and store it in another variable, the following assignment statement could be used:
i = ArrayName (2) ' Read the Third Element (Starting Byte Plus 2)
Writing to an array is carried out exactly the same way. Instead of explicitly specifying the array s index, you can calculate it arithmetically using an expression. For example, the value 47 is written to the seventh element if i is equal to three:
ArrayName (i 2) = 47 ' Write to 7th Element (Starting Byte Plus 6)
Arrays are often used to implement a string of characters. A string is simply a sequence of alphabetic or numeric characters implemented as a series of incrementing array elements. Most strings are of the ASCIIZ type, which means that they consist of a number of ASCII characters and end with the ASCII NULL character (hex $00).
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