Complementary code is a numerical representation commonly used in binary number operations in computers. The complement code simplifies the addition and subtraction operations of negative numbers and can represent a wider range of integers. The use of the complement code plays an important role in computer science and is very important for understanding the operation and representation of integers in computers.
The operating environment of this tutorial: Windows 10 system, Dell G3 computer.
What is the complement code?
's complement is a numerical representation commonly used in binary number operations in computers. In computers, numbers are represented in binary form, a sequence of bits consisting of 0s and 1s. In order for computers to operate on negative numbers, a way to represent negative numbers is needed. Complement is the mathematical concept that accomplishes this.
In binary number operations, there are many ways to represent negative numbers, including original code, complement code and complement code. The original code is the most intuitive and simple method. The sign bit is 1 for negative numbers, 0 for non-negative numbers, and the remaining bits represent the absolute value of the value. However, in the original code representation, the operations of adding and subtracting numbers become very complicated because operations between negative and positive numbers need to take into account carry. To simplify the processing of negative numbers in computers, designers introduced two's complement representation.
The definition of complement code is as follows: the complement code of a positive number is the same as its original code, and the complement code of a negative number is the same as adding its inverse code and adding 1. In other words, the complement of a negative number is obtained by negating its original number (one's complement) and then adding 1. An important property of the two's complement is that for any integer n, its complement is the same as -n's complement. For example, -2's complement is the same as 2's complement.
The design of the complement code allows the computer to use the same adder to add positive and negative numbers, thereby simplifying the operation logic. With two's complement notation, a subtraction operation can be converted into an addition operation by taking the complement of the subtrahend (a negative number) and then adding the operation. In this way, the same hardware circuit can be used to implement addition and subtraction operations.
In addition, the complement representation has another important feature, that is, the range of the complement is one bit larger than the range of the original code and the complement. For example, for an 8-bit binary number, the original and complement codes can represent integers in the range -127 to 127, while the complement code can represent integers in the range -128 to 127. This is because the two's complement code used to represent 0 is the same as for positive numbers.
In short, two's complement is a numerical representation used in computers to perform operations on negative numbers. It simplifies the addition and subtraction of negative numbers while being able to represent a wider range of integers. The use of one's complement plays an important role in computer science and is very important for understanding the operation and representation of integers in computers.
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