In mathematics, an operand is the object of a mathematical operation, a quantity on which
an operation is performed.
Example The following arithmetic expression shows
an example of operators and operands:
In the above example, '+' is the symbol for the operation called addition.
The operand '3' is one of the inputs followed by the addition operator, and the operand
'6' is the other input necessary for the operation. The result of the operation is 9.
An operand, then, is also referred to as "one of the inputs for an operation".
Notation Expressions as operands
Operands may be complex, and may consist of expressions also made up of operators with
operands.
In the above expression '(3 + 5)' is the first operand for the multiplication operator
and '2' the second. The operand '(3 + 5)' is an expression in itself, which contains
an addition operator, with the operands '3' and '5'.
Order of operations
Rules of precedence affect which values form operands for which operators:
In the above expression, the multiplication operator has the higher precedence than the
addition operator, so the multiplication operator has operands of '5' and '2'. The addition
operator has operands of '3' and '5 × 2'. Positioning of operands
Depending on the mathematical notation being used the position of an operator in relation
to its operand(s) may vary. In everyday usage infix notation is the most common, however
other notations also exist, such as the prefix and postfix notations. These alternate notations
are most common within computer science. Below is a comparison of three different notations
— all represent an addition of the numbers '1' and '2'
Infix Notation and the Order of Operation
With infix notation, one easy mnemonic for remembering the order of operation is:
Please excuse my dear Aunt Sally. The first letter of each word in the above
mnemonic stands for the following: p = parentheses
e = exponents m = multiplication
d = division a = addition
s = subtraction In a mathematical expression, the order of
operation is carried out from left to right. Start with the left most value and seek the
first operation to be carried out in accordance with the order specified above. For example,
in the expression ,
the first operation to be acted upon is any and all expressions found inside a parenthesis.
So beginning at the left and moving to the right, find the first parenthesis, that is,.
Within the parenthesis itself is found the expression 22. The reader is required to find
the value of 22 before going any further. The value of 22 is 4. Having found this value,
the remaining expression looks like this:
The next step is to calculate the value of expression inside the parenthesis itself,
that is, = 6. Our expression now looks like this:
Having calculated the parenthetical part of the expression, we start over again beginning
with the left most value and move right. The next order of operation is exponents. Start
at the left most value, that is, 4, and scan your eyes to the right and search for the
first exponent you come across. The first expression we come across that is expressed
with an exponent is 22. We find the value of 22, which is 4. What we have left is the
expression .
The next order of operation is multiplication. 4 × 4 is 16. Now our expression looks like
this:
The next order of operation according to the rules is division. However, there is no division
operator sign in the expression, 16 − 6. So we move on to the next order of operation,
i.e., addition. But there is no addition operator sign in the expression 16 − 6. So we move
on to the next and final order of operation, which is subtraction.
. So the correct value for our original expression,
4 × 22 − (2 + 22), is 10. It is important to carry out the order of
operation in accordance with rules set by convention. If the reader evaluates an expression
but does not follow the correct order of operation, the reader will come forth with a different
value. The different value will be the incorrect value because the order of operation was not
followed. The reader will arrive at the correct value for the expression if and only if each
operation is carried out in the proper order. Arity
The number of operands of an operator is called its arity. Based on arity, operators are classified
as nullary, unary, binary, ternary etc. Computer science
In computer programming languages, the definitions of operator and operand are almost the same
as in mathematics. In computing, an operand is the part of a
computer instruction which specifies what data is to be manipulated or operated on,
while at the same time representing the data itself. A computer instruction describes an
operation such as add or multiply X, while the operand specify on which X to operate
as well as the value of X. Additionally, in assembly language, an operand
is a value on which the instruction, named by mnemonic, operates. The operand may be
a processor register, a memory address, a literal constant, or a label. A simple example
is MOV DS, AX
where the value in register operand 'AX' is to be moved into register 'DS'. Depending
on the instruction, there may be zero, one, two, or more operands.
See also
Instruction set References