2/29/2024 0 Comments Graphing calculator reflectionFor example, the fourth bit of 0010 (decimal 2) may be set by performing a bitwise OR with the pattern with only the fourth bit set: The bitwise OR may be used to set to 1 the selected bits of the register described above. The result in each position is 0 if both bits are 0, while otherwise the result is 1. Using the example above:īecause 6 AND 1 is zero, 6 is divisible by two and therefore even.Ī bitwise OR is a binary operation that takes two bit patterns of equal length and performs the logical inclusive OR operation on each pair of corresponding bits. The third flag may be cleared by using a bitwise AND with the pattern that has a zero only in the third bit:īecause of this property, it becomes easy to check the parity of a binary number by checking the value of the lowest valued bit. This technique is an efficient way to store a number of Boolean values using as little memory as possible.įor example, 0110 (decimal 6) can be considered a set of four flags, where the first and fourth flags are clear (0), and the second and third flags are set (1). The bitwise AND may be used to clear selected bits (or flags) of a register in which each bit represents an individual Boolean state. In this case, the 0 values mask the bits that are not of interest.) (By analogy, the use of masking tape covers, or masks, portions that should not be altered or portions that are not of interest. For example, given a bit pattern 0011 (decimal 3), to determine whether the second bit is set we use a bitwise AND with a bit pattern containing 1 only in the second bit:īecause the result 0010 is non-zero, we know the second bit in the original pattern was set. The operation may be used to determine whether a particular bit is set (1) or cleared (0). Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1) otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). A simple but illustrative example use is to invert a grayscale image where each pixel is stored as an unsigned integer.ĪND Bitwise AND of 4-bit integersĪ bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. For example, for 8-bit unsigned integers, NOT x = 255 - x, which can be visualized on a graph as a downward line that effectively "flips" an increasing range from 0 to 255, to a decreasing range from 255 to 0. If two's complement arithmetic is used, then NOT x = -x − 1.įor unsigned integers, the bitwise complement of a number is the "mirror reflection" of the number across the half-way point of the unsigned integer's range. The result is equal to the two's complement of the value minus one. Bits that are 0 become 1, and those that are 1 become 0. The bitwise NOT, or bitwise complement, is a unary operation that performs logical negation on each bit, forming the ones' complement of the given binary value. For example, the binary value 0001 (decimal 1) has zeroes at every position but the first (i.e., the rightmost) one. In the explanations below, any indication of a bit's position is counted from the right (least significant) side, advancing left. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. For the general concept, see Offset binary. For the excess-3 code, see Shifted binary (code).
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