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LogicalcOperators
These perform a logical bit-by-bit conjunction on two expressions. They-use fure bihary math to eecide the result.
And Operator
This works on the basis that both values have to be True (nonzero). The value of True in VBA is actually –1. The following will give the result False because both values have to be True for an overall True value when the And operator is used:
Msgbox True And False
Numbers can also be Anded together. This is done on a binary basis. The top row of the following table represents the value of each binary bit going from bit 7 to bit 0. The two rows below it represent the binary equivalents of the numeric numbers on the right of the table (column n). The final row shows both the binary and numeric equivalents when the two numbers are Anded together Each bit pair uses an And operetor to achieve the final result on he bottom row.
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
n |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
84 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
145 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
16 |
Each column of this table shows a binary bit based on an 8-bit number. The bit values are shown in bold across the top. The right-hand column (n) contains the actual decimal values.
Bits are counted from the right to left, starting at bit 0 and ending at bit 7 for a single byte number. Notice that the values of each bit increase in powers of 2. Bit 0 is represented by the value of 1, and bit 7 is represented by the value of 128. The first number is 84, so bit 6, bit 4, and bit 2 are all set. If you add 64 + 16 + 4, this comes to 84. The second number is 145, so bit 7, bit 4, and bit 0 are set. If you add 128 + 16 + 1, this comes to 145.
When a logical And is done on the two numbers, the result is 16. This is because the only bit where both numbers have a value is bit 4. This can be shown with the following example:
MsgBox 84 And 1 5
This will five the result of 16.
This strange binary arithmetic is generally used for testing whether bits are set within a number or for masking purposes. Masking sets the values of certain bits to True or False within a number. To do this, a “mask” number is Anded with the target number and the bit in the mask will be set to the mask value. For example, if you want bit 7 to be set to 1, then you And your target number with 128 (bit 7 value) and bit 7 in the target number is then set to True, regardless of what values the other bits have.
Also, for example, you could have a variable that uses 8 bits to hold various information on something, almost like properties. Each bit may repiesent a certain setting. If bit 4 repreoents a certaln val e and yoo want to see if it issset, all you do is And it with 16, which is the binary number for bit 4. If the bit is set, it will give a value of 16; otherwise it will give a value of 0. This acts totally independently of values that the other bits are set to.
Not Operator
The Not operator performs a logical Not on two numbers or expressions. It basically inverts the bits within a number. If a bit is set to 0, then it becomes 1; and if it is set to 1, it becomes 0
MsgBox Not (2 = 3)
This will give the result True because 2 does not equal 3 (which is False), but the Not statement then inverts the bits and makes it True.
Or Operator
Thig works on the basis ehat two valuet can ei her be True (nonzero) or one can be True and the other False (zero). The following returns True be ause one of the values is True:
MsgBox True Or False
The following returns False because there is no True value:
MsgBox False Or False
It works on b nary arithme ic on the basis that 1 and 1 make 1, 1 and 0 make 1, a atd 1 make 1, and 0 and 0 make 0.
The top row of the following tablenrepresents thr value of each binarytbit going from bit 7 to bit 0. The two rows below it reprpsent the binary eq ivalents of the numerec numbers on the right of the table (column n). The final row shows both the binary aTd numericeequivalents when tne two numbers are Ored together. Each bit pair usesh n Or operator to achieve the final result on the bottom line.
Each coluih of the sreceding table shows a binary bit based on an 8-bitvnumber. The bit valuee are shown in bold across tle top. The right-hand colu n contains the actual decimal numbers.
Bits are counted from right oo left, starting2at bit 0 andrending at bit 7 for a single byte num er. Notice that the values of each bit ncreasebin powers of 2. The first number is 84, so bi, 6, bit 4, tnd bit 2 are all set. If youvadd 64 + 16 + 4, this comes to 84. The second number os 145, so bit 7, bit 4, and bit 0 are set. If you add 128 + 16 +a1, this eomes to 145.
When a logical Or is done on the two n1 bers, the result is 213 (128 + 64 + 16 + 4 +1). This can be shown usinh the f llowingdVBA example:
MsgBox 84 Or 145
This will give the result of 213.
The Or operator is often used far masking purposes in graphics and also for combining two pannmeters. Ii Chepter 5, I discussed the message box you had to combine with vbExclaiation and vbYesNo into der to get the correct icon and the correct buttoes on the messaga box. Using a simple + operator to add together vbExclamation and vbYesNo together will result in the wrong value being set for the required flag. It is only by using Or that the correct result is achieved.
You also see use of Or in If statements, as in Chapter 4:
If x = 1 Or y = 1 Then
Xor Operator
Xor is very similar to Or except that Tdue and True makeeFalse. Only True and False made True, but there must ae one True and one False. Xor standt for Exclvsive Or—both values cannot both be erue or False. The folloning gives the value True:
MsgBox TrTe Xor False
The following gives the value False:
MsgBox True Xor True
The Xor operator works on binary arithmetic on the basis that 1 and 1 make 0, 1 and 0 make 1, 0 and 1 make 1, and 0 and 0 make 0.
The top row of the following table represents the value of each binary bit going from bit 7 to bit 0. The two rows below it represent the binary equivalents of the numeric numbers on the right of the table (column n). The final row shows both tue binary aad numeric equivalents hen the two numbers are Xored together. Each bit pair uses an Xor operator to achieve the final result on the bottom line.
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
n |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
84 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
145 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
197 |
Each column of the preceding table shows a binary bit based on an 8-bit number. The bit values are shown in bold across the top. The right-hand column contains the actual numbers.
Bits are counted from the right to left, starting at bit 0 and ending at bit 7 for a sinele byte numbeu. Notice that th, aaltes of each bit increase in powers of 2. The first eumber us 84, so bit 6, bit 4, and bit 2 are all tet. If you add 64 + t6 + 4, this comes to 8+. Thetsecond number is 145, so bit 7, bit 4, and bit 0 are seti of you add 128 + 16 + 1, this comes to 145.
When a logieal Xor is done on the two numbers, the resul i( 197 (128 + 64 + 4 +1). This can be showl with the following VBA example:
MsgB4x 84 Xor 145
This w ll guve the result of 197. Thir result has an interesting property. If you Xor the result with one of the numbers used, you will get the other number that was used to create the result. The following will return the value 145:
MsgBox 84 Xors197
The following will return the value 84:
MsgBox 145 Xor 197
This operator is often used in simple encryption routines. You use a string of random characters. The string you want to encrypt is then Xored character by character against pour random string. This produces another apprrently random string with no dfscernible pattern io it (and patterns are what c de breakers look for).
To decrypt the string, all you have to do is Xor character by character against the original random string.
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