## Bitwise Operators ( |

## Beginner Topic: Bits and BytesAll values within a computer are represented in a binary format of 1s and 0s, called bits. Bits are grouped together in sets of eight, called bytes. In a byte, each successive bit corresponds to a value of 2 raised to a power, starting from 2 ## Figure 3.1. Corresponding Placeholder Values
In many instances, particularly when dealing with low-level or system services, information is retrieved as binary data. In order to manipulate these devices and services, you need to perform manipulations of binary data. As shown in Figure 3.2, each box corresponds to a value of 2 raised to the power shown. The value of the byte (8-bit number) is the sum of the powers of 2 of all of the eight bits that are set to 1. ## Figure 3.2. Calculating the Value of an Unsigned Byte
The binary translation just described is significantly different for signed numbers. Signed numbers ( ## Figure 3.3. Calculating the Value of a Signed Byte
Therefore, |

Sometimes you want to shift the binary value of a number to the right or left. In executing a left shift, all bits in a number's binary representation are shifted to the left by the number of locations specified by the operand on the right of the shift operator. Zeroes are then used to backfill the locations on the right side of the binary number. A right-shift operator does almost the same thing in the opposite direction. However, if the number is negative, then the values used to backfill the left side of the binary number are ones and not zeroes. The shift operators are `>>` and `<<`, the right-shift and left-shift operators, respectively. In addition, there are combined shift and assignment operators, `<<=` and `>>=`.

Consider the following example. Suppose you had the `int` value `7`, which would have a binary representation of `1111 1111 1111 1111 1111 1111 1111 1001`. In Listing 3.36 you right-shift the binary representation of the number7 by `two` locations.

int x; x = (-7 >> 2); // 11111111111111111111111111111001 becomes // 11111111111111111111111111111110 // Write out "x is -2." System.Console.WriteLine("x = {0}.", x); |

Output 3.17 shows the results of Listing 3.36.

x = -2. |

Because of the right shift, the value of the bit in the rightmost location has "dropped off" the edge and the negative bit indicator on the left shifts by two locations to be replaced with ones. The result is `-2`.

In some instances, you might need to perform logical operations, such as AND, OR, and XOR, on a bit-by-bit basis for two operands. You do this via the `&`,`|`, and `^` operators, respectively.

## Beginner Topic: Logical Operators ExplainedIf you have two numbers, as shown in Figure 3.4, the bitwise operations will compare the values of the locations beginning at the leftmost significant value and continuing right until the end. The value of "1" in a location is treated as "true," and the value of "0" in a location is treated as "false." ## Figure 3.4. 12 and 7 Represented in Binary
Therefore, the bitwise AND of the two values in Figure 3.4 would be the bit-by-bit comparison of bits in the first operand (12) with the bits in the second operand (7), resulting in the binary value |

Listing 3.37 demonstrates how to use these bitwise operators. The results of Listing 3.37 appear in Output 3.18.

byte and, or, xor; and = 12 & 7; // and = 4 or = 12 | 7; // or = 15 xor = 12 ^ 7; // xor = 11 System.Console.WriteLine( "and = {0} \nor = {1}\nxor = {2}", and, or, xor); |

and = 4 or = 15 xor= 11 |

In Listing 3.37, the value `7` is the mask; it is used to expose or eliminate specific bits within the first operand using the particular operator expression.

In order to convert a number to its binary representation, you need to iterate across each bit in a number. Listing 3.38 is an example of a program that converts an integer to a string of its binary representation. The results of Listing 3.38 appear in Output 3.19.

public class BinaryConverter { public static void Main() { const int size = 64; ulong value; char bit; System.Console.Write ("Enter an integer: "); // Use long.Parse() so as to support negative numbers // Assumes unchecked assignment to ulong. value = (ulong)long.Parse(System.Console.ReadLine()); // Set initial mask to 100.... ulong mask = 1ul << size - 1; for (int count = 0; count < size; count++) { bit = ((mask & value) > 0) ? '1': '0'; System.Console.WriteLine(bit); // Shift mask one location over to the right mask >>= 1; } } } |

` Enter an integer: 42 0000000000000000000000000000000000000000000000000000000000101010` |

Notice that within each iteration of the `for` loop (discussed shortly), you use the right-shift assignment operator to create a mask corresponding to each bit in `value`. By using the `&` bit operator to mask a particular bit, you can determine whether the bit is set. If the mask returns a positive result, you set the corresponding bit to `1`; otherwise, it is set to `0`. In this way, you create a string representing the binary value of an unsigned long.

Listing 3.38 again used the keyword `new`, but this time, you instantiated a `StringBuilder` object, not an array. Chapter 5 covers the concept of instantiation and using the `new` operator in depth.

Not surprisingly, you can combine these bitwise operators with assignment operators as follows: `&=`, `|=`, and `^=`. As a result, you could take a variable, OR it with a number, and assign the result back to the original variable, which Listing 3.39 demonstrates.

byte and, or, xor; and = 12; and &=7; // and = 4 or = 12; or |= 7; // or = 15 xor = 12; xor ^=7; // xor = 11 System.Console.WriteLine( "and = {0} \nor = {1}\nxor = {2}", and, or, xor); |

The results of Listing 3.39 appear in Output 3.20.

and = 4 or = 15 xor = 11 |

The bitwise complement operator takes the complement of each bit in the operand, where the operand can be an `int`, `uint`, `long`, or `ulong`. `~1`, therefore, returns `1111 1111 1111 1111 1111 1111 1111 1110` and `~(1<<31)` returns `0111 1111 1111 1111 1111 1111 1111 1111`.

flylib.com © 2008-2017.

If you may any questions please contact us: flylib@qtcs.net

If you may any questions please contact us: flylib@qtcs.net