Representasi Bilangan dalam Algoritma dan Pemrograman
The realm of algorithms and programming hinges on the fundamental concept of representing numbers. Understanding how numbers are represented within a computer system is crucial for comprehending the inner workings of algorithms and writing efficient code. This article delves into the various methods of representing numbers in algorithms and programming, exploring their strengths, weaknesses, and practical applications.
Binary Representation: The Foundation of Computing
At the heart of computer systems lies the binary system, a numerical system that uses only two digits: 0 and 1. This system forms the bedrock of representing numbers in computers. Each digit in a binary number, known as a bit, represents a power of two. For instance, the binary number 1011 translates to (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11 in decimal form. This binary representation allows computers to process information efficiently using electronic circuits that can represent either a high or low voltage, corresponding to 1 or 0.
Integer Representation: Representing Whole Numbers
Integers, whole numbers without fractional parts, are commonly represented using two's complement notation. This method utilizes the most significant bit (MSB) to indicate the sign of the number. A 0 in the MSB signifies a positive number, while a 1 indicates a negative number. The remaining bits represent the magnitude of the number. For example, in an 8-bit system, the binary representation of -5 would be 11111011, where the MSB is 1, indicating a negative number, and the remaining bits represent the magnitude 5.
Floating-Point Representation: Handling Fractional Numbers
Floating-point numbers, which include fractional parts, are represented using a standardized format called IEEE 754. This format divides the number into three parts: the sign bit, the exponent, and the mantissa. The sign bit indicates the number's sign, the exponent determines the magnitude, and the mantissa represents the fractional part. This representation allows for a wide range of numbers, from extremely small to extremely large, but introduces limitations in precision and can lead to rounding errors.
Character Representation: Encoding Textual Data
Computers store textual data using character encoding schemes, such as ASCII and Unicode. These schemes assign unique numerical values to each character, allowing computers to represent and manipulate text. ASCII uses 7 bits to represent 128 characters, including uppercase and lowercase letters, numbers, punctuation marks, and control characters. Unicode, a more comprehensive system, uses 16 or 32 bits to represent a vast range of characters from different languages and scripts.
Conclusion
The representation of numbers forms the foundation of algorithms and programming. Understanding the different methods of representing numbers, including binary, integer, floating-point, and character encoding, is crucial for comprehending how computers process information and for writing efficient and accurate code. Each representation has its strengths and weaknesses, and choosing the appropriate method depends on the specific requirements of the algorithm or program. By mastering these fundamental concepts, programmers can unlock the full potential of computer systems and develop innovative solutions to complex problems.