Bitwise operation

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There are four main logical operations we'll need to perform on hexadecimal and binary numbers: Unlike the arithmetic operations, a hexadecimal calculator isn't necessary to perform these operations. Anding 2 binary values base is often easier to do them by hand than to use an electronic device to compute them. The logical AND operation is a dyadic 1 operation meaning it accepts exactly two operands. These operands are single binary base 2 bits.

The AND operation is:. A compact way to represent the logical AND operation is with a truth table. A truth table takes the following form:. This is just like the multiplication tables you encountered in elementary school. The values in the left column correspond to the leftmost operand of the Anding 2 binary values base operation.

The values in the top row correspond to the rightmost anding 2 binary values base of the AND operation. The value located at the intersection of the row and column for a particular pair of input values is the result of logically ANDing those two values together.

In English, the logical AND operation is, "If the first operand is one and the second operand is one, the result is one; anding 2 binary values base the result is zero. One important fact to note about the logical AND operation is that you can use it to force a zero result. If one of the operands is zero, the result is always zero regardless of the other anding 2 binary values base. In the truth table above, for example, the row labelled with a zero input contains only zeros and the column labelled with a zero only anding 2 binary values base zero results.

Conversely, if one operand contains a one, the result is exactly the value of the second operand. These features of the AND operation are very important, particularly when we want to force individual bits in a bit string to zero. We will investigate these uses of the logical AND operation in the next section. The logical OR operation is also a dyadic operation. The truth table for the OR operation takes the following form: Colloquially, the logical OR operation is, "If the first operand or anding 2 binary values base second operand or both is one, the result is one; otherwise the result is zero.

If one of the operands to the logical-OR operation is a one, the result is always one regardless of the second operand's value. If one operand is zero, the result is always the value of the second operand. Like the logical AND operation, this is an important side-effect of the logical-OR operation that will prove quite useful when working with bit strings since it lets you force individual bits to one.

Note that there is a difference between this form of the inclusive logical OR operation and the standard English meaning. Consider the phrase "I am going to the store or I am going to the park. Therefore, the English version of logical OR is slightly different than the inclusive-OR operation; indeed, it is closer to the exclusive-OR operation.

The logical XOR exclusive-or operation is also a dyadic operation. It is defined as follows:. The truth table for the XOR operation takes the following form:. In English, the logical XOR operation is, "If the first operand or the second operand, but not both, is one, the result is anding 2 binary values base otherwise the result is zero. If one of the operands to the logical exclusive-OR operation is a one, the result is always the inverse of the other operand; that is, if one operand is one, the result is zero if the other operand is one and the result is one if the other operand is zero.

If the first operand contains a zero, then the result is exactly the value of the second operand. This feature lets you selectively invert bits in a bit string. The logical NOT operation is a monadic operation meaning it accepts only one operand.

The truth table for the NOT operation takes the following form:. As described in the previous section, the logical functions work only with single bit operands. Since the 80x86 uses groups of eight, sixteen, or thirty-two bits, we need to extend the definition of these functions to deal with more than two bits. Logical functions on the 80x86 operate on a bit-by-bit or bitwise basis.

Given two values, these functions operate on bit zero producing bit zero of the result. They operate on bit one of the input values producing bit one of the result, etc. For example, if you want to compute the logical AND of the following two eight-bit numbers, you would perform the logical AND operation on each column independently of the others:. This bit-by-bit form of execution can be easily applied to the other logical operations as well.

Since we've defined logical operations in terms of binary values, you'll find it much easier to perform logical operations on binary values than on values in other bases. Therefore, if you want to perform a logical operation on two hexadecimal numbers, you should convert them to binary first.

This anding 2 binary values base to most of the basic logical operations on binary numbers e. These operations let you selectively manipulate certain bits within some value while leaving other bits unaffected.

This bitwise logical AND operation would force the H. Likewise, you could force the L. The 80x86 CPUs support four instructions that apply these bitwise logical operations to their operands. These operands have the same limitations as the ADD operands. Specifically, the source operand has to be a constant, memory, or register operand and the dest operand must be a memory or register operand.

Also, the operands must be the same size and they cannot both be memory operands. These instructions compute the obvious bitwise logical operation via the equation:. The 80x86 logical NOT instruction, since it has only a single operand, uses a slightly different syntax.

This instruction takes the following form:. Note that this instruction has a single operand. It computes the following result:. The dest operand for not must be a register or memory operand. This instruction inverts all the bits in the specified destination operand.

The term dyadic means anding 2 binary values base same thing and avoids the confusion with the binary anding 2 binary values base system. Web Site Hits Since Jan 1,

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Bitwise operators treat their operands as a sequence of 32 bits zeroes and ones , rather than as decimal, hexadecimal, or octal numbers. For example, the decimal number nine has a binary representation of Bitwise operators perform their operations on such binary representations, but they return standard JavaScript numerical values.

The source for this interactive example is stored in a GitHub repository. If you'd like to contribute to the interactive examples project, please clone https: The operands of all bitwise operators are converted to signed bit integers in two's complement format. Two's complement format means that a number's negative counterpart e. For example, the following encodes the integer The two's complement guarantees that the left-most bit is 0 when the number is positive and 1 when the number is negative.

Thus, it is called the sign bit. The number hexadecimal representation: The numbers and are the minimum and the maximum integers representable through a 32bit signed number. Performs the AND operation on each pair of bits. The truth table for the AND operation is:.

Bitwise ANDing any number x with 0 yields 0. Bitwise ANDing any number x with -1 yields x. Performs the OR operation on each pair of bits. The truth table for the OR operation is:. Bitwise ORing any number x with 0 yields x.

Bitwise ORing any number x with -1 yields Performs the XOR operation on each pair of bits. The truth table for the XOR operation is:. Bitwise XORing any number x with 0 yields x. Performs the NOT operator on each bit. NOT a yields the inverted value a. The truth table for the NOT operation is:. The bitwise shift operators take two operands: The direction of the shift operation is controlled by the operator used.

Shift operators convert their operands to bit integers in big-endian order and return a result of the same type as the left operand.

The right operand should be less than 32, but if not only the low five bits will be used. This operator shifts the first operand the specified number of bits to the left. Excess bits shifted off to the left are discarded. Zero bits are shifted in from the right. This operator shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded.

Copies of the leftmost bit are shifted in from the left. Since the new leftmost bit has the same value as the previous leftmost bit, the sign bit the leftmost bit does not change. Hence the name "sign-propagating". Zero bits are shifted in from the left.

The sign bit becomes 0, so the result is always non-negative. For non-negative numbers, zero-fill right shift and sign-propagating right shift yield the same result.

However, this is not the case for negative numbers. The bitwise logical operators are often used to create, manipulate, and read sequences of flags , which are like binary variables.

Variables could be used instead of these sequences, but binary flags take much less memory by a factor of These flags are represented by a sequence of bits: When a flag is set , it has a value of 1. When a flag is cleared , it has a value of 0. Suppose a variable flags has the binary value Since bitwise operators are bit, is actually , but the preceding zeroes can be neglected since they contain no meaningful information.

Typically, a "primitive" bitmask for each flag is defined:. New bitmasks can be created by using the bitwise logical operators on these primitive bitmasks. Individual flag values can be extracted by ANDing them with a bitmask, where each bit with the value of one will "extract" the corresponding flag. The bitmask masks out the non-relevant flags by ANDing with zeroes hence the term "bitmask".

For example, the following two are equivalent:. Flags can be set by ORing them with a bitmask, where each bit with the value one will set the corresponding flag, if that flag isn't already set. For example, the bitmask can be used to set flags C and D:. Flags can be cleared by ANDing them with a bitmask, where each bit with the value zero will clear the corresponding flag, if it isn't already cleared.

This bitmask can be created by NOTing primitive bitmasks. For example, the bitmask can be used to clear flags A and C:. Flags can be toggled by XORing them with a bitmask, where each bit with the value one will toggle the corresponding flag. For example, the bitmask can be used to toggle flags B and C:. Convert a binary String to a decimal Number:. Convert a decimal Number to a binary String:. If you want to create an Array of Booleans from a mask you can use this code:. For didactic purpose only since there is the Number.

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I'm okay with Mozilla handling my info as explained in this Privacy Policy. Please check your inbox to confirm your subscription. Returns a 1 in each bit position for which the corresponding bits of both operands are 1 's.

Returns a 1 in each bit position for which the corresponding bits of either or both operands are 1 's. Returns a 1 in each bit position for which the corresponding bits of either but not both operands are 1 's. Defined in several sections of the specification: Bitwise OR a b.