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You cannot use bitwise operations on float , double, long double, void , or other more complex types Table 2-6 lists the operators that apply to bitwise operations These operations are applied to the individual bits of the operands The bitwise AND, OR, and NOT (one's complement) are governed by the same truth table as their logical equivalents, except that they work bit by bit The exclusive OR has the truth table shown here: p 0 1 1 0 q 0 0 1 1 p ^q 0 1 0 1
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As the table indicates, the outcome of an XOR is true only if exactly one of the operands is true; otherwise, it is false Bitwise operations most often find application in device drivers such as modem programs, disk file routines, and printer routines because the bitwise operations can be used to mask off certain bits, such as parity (The parity bit confirms that the rest of the bits in the byte are unchanged It is often the high-order bit in each byte)
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Operator & | ^ ~ >> << Table 2 -6 Bitwise Operators Action AND OR Exclusive OR (XOR) One's complement (NOT) Shift right Shift left
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Think of the bitwise AND as a way to clear a bit That is, any bit that is 0 in either operand causes the corresponding bit in the outcome to be set to 0 For example, the following function reads a character from the modem port and resets the parity bit to 0:
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char get_char_from_modem(void) { char ch; ch = read_modem(); /* get a character from the modem port */ return(ch & 127); }
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Parity is often indicated by the eighth bit, which is set to 0 by ANDing it with a byte that has bits 1 through 7 set to 1 and bit 8 set to 0 The expression ch & 127 means to AND together the bits in ch with the bits that make up the number 127 The net result is that the eighth bit of ch is set to 0 In the following example, assume that ch had received the character A and had the parity bit set:
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The bitwise OR, as the reverse of AND, can be used to set a bit Any bit that is set to 1 in either operand causes the corresponding bit in the outcome to be set to 1 For example, the following is 128 | 3:
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An exclusive OR, usually abbreviated XOR, will set a bit on, if and only if the bits being compared are different For example, 127 ^120 is
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Remember, relational and logical operators always produce a result that is either true or false, whereas the similar bitwise operations may produce any arbitrary value in accordance with the specific operation In other words, bitwise operations may produce values other than 0 or 1, while logical operators will always evaluate to 0 or 1 The bit-shift operators, >> and <<, move all bits in a variable to the right or left as specified The general form of the shift-right statement is variable >> number of bit positions The general form of the shift-left statement is variable << number of bit positions As bits are shifted off one end, zeroes are brought in the other end (In the case of a signed, negative integer, a right shift will cause a 1 to be brought in so that the sign bit is preserved) Remember, a shift is not a rotate That is, the bits shifted off one end do not come back around to the other The bits shifted off are lost Bit-shift operations can be very useful when you are decoding input from an external device, such as a D/A converter, and reading status information The bitwise shift operators can also quickly multiply and divide integers A shift right effectively divides a number by 2 and a shift left multiplies it by 2, as shown in Table 2-7 The following program illustrates the shift operators:
/* A bit shift example */ #include <stdioh> int main(void) { unsigned int i; int j; i = 1; /* left shifts */ for(j=0; j<4; j++) { i = i << 1; /* left shift i by 1, which is same as a multiply by 2 */ printf(''Left shift %d: %d\n", j, i); } /* right shifts */ for(j=0; j<4; j++) { i = i >> 1; /* right shift i by 1, which
Page 52 is same as a division by 2 */ printf(''Right shift %d: %d\n", j, i); } return 0; }
The one's complement operator, ~, reverses the state of each bit in its operand That is, all 1's are set to 0, and all 0's are set to 1 The bitwise operators are often used in cipher routines If you want to make a disk file appear unreadable, perform some bitwise manipulations on it One of the simplest methods is to complement each byte by using the one's complement to reverse each bit in the byte, as is shown here:
Notice that a sequence of two complements in a row always produces the original number Hence, the first complement represents the coded version of that byte The second complement decodes the byte to its original value
unsigned char x; x = 7; x = x<<l; x = x<<3; x = x<<2; x = x>>l; x = x>>2; x as each statement executes 00000111 00001110 01110000 11000000 01100000 00011000 value of x 7 14 112 192 96 24
Each left shift multiplies by 2 Notice that information has been lost after x<<2 because a bit was shifted off the end Each right shift divides by 2 Notice that subsequent divisions do not bring back any lost bits Table 2 -7 Multiplication and Division with Shift Operators
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