Carry
Encyclopedia
In elementary arithmetic
a carry is a digit
that is transferred from one column
of digits to another column of more significant digits during a calculation algorithm
. When used in subtraction the operation is called a borrow. It is a central part of traditional mathematics
, but is often omitted from curricula based on reform mathematics
, which do not emphasize any specific method to find a correct answer.
:
¹
27
+ 59
----
86
7 + 9 = 16, and the digit 1 is the carry.
The opposite is a borrow, as in
−1
47
− 19
----
28
Here, 7 − 9 = −2, so try (10 − 9) + 7 = 8, and the 10 is got by taking ("borrowing") 1 from the next digit to the left. There are two ways in which this is commonly taught:
omitted instruction of the traditional carry method in favor of invented arithmetic methods, and methods using coloring, manipulatives, and charts. Such omissions were criticized by such groups as Mathematically Correct
, and some states and districts have since abandoned this experiment, though it remains widely used.
like an adder
, the word carry is used in a similar sense. In most computer
s, the carry from the most significant bit of an arithmetic operation (or bit shifted out from a shift operation) is placed in a special carry bit which can be used as a carry-in for multiple precision arithmetic or tested and used to control execution of a computer program
.
Elementary arithmetic
Elementary arithmetic is the simplified portion of arithmetic which is considered necessary and appropriate during primary education. It includes the operations of addition, subtraction, multiplication, and division. It is taught in elementary school....
a carry is a digit
Digit
Digit may refer to:* Digit , one of several most distal parts of a limb—fingers, thumbs, and toes on hands and feet* Numerical digit, as used in mathematics or computer science* Hexadecimal, representing a four-bit number...
that is transferred from one column
Column
A column or pillar in architecture and structural engineering is a vertical structural element that transmits, through compression, the weight of the structure above to other structural elements below. For the purpose of wind or earthquake engineering, columns may be designed to resist lateral forces...
of digits to another column of more significant digits during a calculation algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
. When used in subtraction the operation is called a borrow. It is a central part of traditional mathematics
Traditional mathematics
Traditional mathematics is a term used to describe the predominant methods of Mathematics education in the United States in the early-to-mid 20th century. The term is often used to contrast historically predominant methods with non-traditional approaches to math education...
, but is often omitted from curricula based on reform mathematics
Reform mathematics
Reform mathematics is an approach to mathematics education, particularly in North America. It is based on principles explained in 1989 by the National Council of Teachers of Mathematics . The NCTM document, Curriculum and Evaluation Standards for School Mathematics, attempted to set forth a vision...
, which do not emphasize any specific method to find a correct answer.
Manual arithmetic
A typical example of carry is in the following pencil-and-paper additionAddition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
:
¹
27
+ 59
----
86
7 + 9 = 16, and the digit 1 is the carry.
The opposite is a borrow, as in
−1
47
− 19
----
28
Here, 7 − 9 = −2, so try (10 − 9) + 7 = 8, and the 10 is got by taking ("borrowing") 1 from the next digit to the left. There are two ways in which this is commonly taught:
- The ten is moved from the next digit left, leaving in this example 3 − 1 in the tens column. According to this method, the term "borrow" is a misnomerMisnomerA misnomer is a term which suggests an interpretation that is known to be untrue. Such incorrect terms sometimes derive their names because of the form, action, or origin of the subject becoming named popularly or widely referenced—long before their true natures were known.- Sources of misnomers...
, since the ten is never paid back. - The ten is copied from the next digit left, and then 'paid back' by adding it to the subtrahend in the column from which it was 'borrowed', giving in this example 4 − (1 + 1) in the tens column.
Mathematics education
Traditionally, carry is taught in the addition of multi-digit numbers in the 2nd or late first year of elementary school. However since the late 20th century, many widely adopted curricula developed in the United States such as TERCTERC
TERC may refer to:*Telomerase RNA component, a human gene.*The developers of the Investigations in Numbers, Data, and Space mathematics curriculum.*Technical Education Research Centers*CSIRO Tropical Ecosystems Research Centre...
omitted instruction of the traditional carry method in favor of invented arithmetic methods, and methods using coloring, manipulatives, and charts. Such omissions were criticized by such groups as Mathematically Correct
Mathematically Correct
Mathematically Correct is a website created by educators, parents, mathematicians, and scientists who were concerned about the direction of reform mathematics curricula based on NCTM standards...
, and some states and districts have since abandoned this experiment, though it remains widely used.
Computing
When speaking of a digital circuitDigital circuit
Digital electronics represent signals by discrete bands of analog levels, rather than by a continuous range. All levels within a band represent the same signal state...
like an adder
Adder (electronics)
In electronics, an adder or summer is a digital circuit that performs addition of numbers.In many computers and other kinds of processors, adders are used not only in the arithmetic logic unit, but also in other parts of the processor, where they are used to calculate addresses, table indices, and...
, the word carry is used in a similar sense. In most computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
s, the carry from the most significant bit of an arithmetic operation (or bit shifted out from a shift operation) is placed in a special carry bit which can be used as a carry-in for multiple precision arithmetic or tested and used to control execution of a computer program
Computer program
A computer program is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute...
.