Bitwise Operators (, , , , , )

Bitwise Operators (<<, >>, |, &, ^, ~)

An additional set of operators that is common to virtually all programming languages is the set of operators for manipulating values in their binary formats: the bit operators.

Beginner Topic: Bits and Bytes

All 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 2⁰ on the right, to 2⁷ on the left, as shown in Figure 3.1.

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 (long, short, int) are represented using a 2s complement notation. With this notation, negative numbers behave differently than positive numbers. Negative numbers are identified by a 1 in the leftmost location. If the leftmost location contains a 1, you add the locations with 0s rather than the locations with 1s. Each location corresponds to the negative power of 2 value. Furthermore, from the result, it is also necessary to subtract 1. This is demonstrated in Figure 3.3.

Figure 3.3. Calculating the Value of a Signed Byte

Therefore, 1111 1111 1111 1111 corresponds to a1 and 1111 1111 1111 1001 holds the value7. 1000 0000 0000 0000 corresponds to the lowest negative value that a 16-bit integer can hold.

Shift Operators (<<, >>, <<=, >>=)

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.

Listing 3.36. Using the Right-Shift Operator

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.

Output 3.17.

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.

Bitwise Operators (&, |, ^)

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 Explained

If 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 000000100, which is 4. Alternatively, a bitwise OR of the two values would produce 00001111, the binary equivalent of 15. The XOR result would be 00001011, or decimal 11.

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

Listing 3.37. Using Bitwise Operators

 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);

Output 3.18.

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.

Listing 3.38. Getting a String Representation of a Binary Display

 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;      }   } }

Output 3.19.

 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.

Bitwise Assignment Operators (&=, |=, ^=)

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.

Listing 3.39. Using Logical Assignment Operators

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.

Output 3.20.

and = 4 or = 15 xor = 11

Bitwise Complement Operator (~)

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.