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Operators
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The reason Java (and most other computer languages) uses two s complement is easy to see when you consider the issue of zero crossing Assuming a byte value, zero is represented by 00000000 In one s complement, simply inverting all of the bits creates 11111111, which creates negative zero The trouble is that negative zero is invalid in integer math This problem is solved by using two s complement to represent negative values When using two s complement, 1 is added to the complement, producing 100000000 This produces a 1 bit too far to the left to fit back into the byte value, resulting in the desired behavior, where 0 is the same as 0, and 11111111 is the encoding for 1 Although we used a byte value in the preceding example, the same basic principle applies to all of Java s integer types Because Java uses two s complement to store negative numbers and because all integers are signed values in Java applying the bitwise operators can easily produce unexpected results For example, turning on the high-order bit will cause the resulting value to be interpreted as a negative number, whether this is what you intended or not To avoid unpleasant surprises, just remember that the high-order bit determines the sign of an integer no matter how that high-order bit gets set
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The Bitwise Logical Operators
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The bitwise logical operators are &, |, ^, and ~ The following table shows the outcome of each operation In the discussion that follows, keep in mind that the bitwise operators are applied to each individual bit within each operand
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A 0 1 0 1 B 0 0 1 1 A|B 0 1 1 1 A&B 0 0 0 1 A^B 0 1 1 0 ~A 1 0 1 0
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The Bitwise NOT
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Also called the bitwise complement, the unary NOT operator, ~, inverts all of the bits of its operand For example, the number 42, which has the following bit pattern: 00101010 becomes 11010101 after the NOT operator is applied
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The Bitwise AND
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The AND operator, &, produces a 1 bit if both operands are also 1 A zero is produced in all other cases Here is an example: 00101010 & 00001111 00001010 42 15 10
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Part I:
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The Java Language
The Bitwise OR
The OR operator, |, combines bits such that if either of the bits in the operands is a 1, then the resultant bit is a 1, as shown here: 00101010 | 00001111 00101111 42 15 47
The Bitwise XOR
The XOR operator, ^, combines bits such that if exactly one operand is 1, then the result is 1 Otherwise, the result is zero The following example shows the effect of the ^ This example also demonstrates a useful attribute of the XOR operation Notice how the bit pattern of 42 is inverted wherever the second operand has a 1 bit Wherever the second operand has a 0 bit, the first operand is unchanged You will find this property useful when performing some types of bit manipulations 00101010 ^ 00001111 00100101 42 15 37
Using the Bitwise Logical Operators
The following program demonstrates the bitwise logical operators:
// Demonstrate the bitwise logical operators class BitLogic { public static void main(String args[]) { String binary[] = { "0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111" }; int a = 3; // 0 + 2 + 1 or 0011 in binary int b = 6; // 4 + 2 + 0 or 0110 in binary int c = a | b; int d = a & b; int e = a ^ b; int f = (~a & b) | (a & ~b); int g = ~a & 0x0f; Systemoutprintln(" a Systemoutprintln(" b Systemoutprintln(" a|b Systemoutprintln(" a&b Systemoutprintln(" a^b Systemoutprintln("~a&b|a&~b Systemoutprintln(" ~a } } = = = = = = = " " " " " " " + + + + + + + binary[a]); binary[b]); binary[c]); binary[d]); binary[e]); binary[f]); binary[g]);
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