Data Representation in Computing

A method of representing negative numbers in binary by inverting all the bits (0s become 1s and 1s become 0s) of the positive number and then adding 1. For example, the one's complement of 0101 is 1010.

A way of representing negative numbers in binary by inverting all the bits of the positive number and then adding 1 to the result. It is similar to one's complement but includes an extra step of adding 1.

A way of classifying the magnitude of binary numbers using prefixes like Kilo-, Mega-, Giga-, etc. These prefixes are based on powers of 2, similar to how the prefixes in the decimal system are based on powers of 10.

A system of representing numbers using base 16. It uses digits 0-9 and letters A-F to represent values from 0 to 15. One hexadecimal digit represents four binary bits.

The number system used by computers, utilizing only two digits (0 and 1) to represent any number.

A system where each digit's position has a specific weight, determining its value in the overall number. This weight is often a power of the base.

The process of converting a binary number to its decimal (base 10) equivalent.

The most significant bit (MSB) determines if the number is positive or negative. A 0 signifies positive, while a 1 signifies negative.

This is a system where the leftmost digit in a binary number indicates the sign of the number. 0 for positive, 1 for negative. Its value is -127. The value of each position increases from 1 to 127.

The binary equivalent of a decimal number is created by repeatedly dividing the decimal number by 2 and recording the remainders (either 0 or 1). The remainders, read from bottom to top, form the binary representation.

Converting a hexadecimal number to decimal involves multiplying each digit by its corresponding power of 16 and summing the results. For example, 2AF in hexadecimal translates to (2 * 256) + (10 * 16) + (15 * 1) = 687 in decimal.

Binary Coded Decimal (BCD) is a system where each decimal digit is represented by a 4-bit binary code. For example, the number 316 would be represented as 0011 0001 0110.

ASCII (American Standard Code for Information Interchange) is a standard that assigns numerical values to characters and symbols, allowing computers to process and manipulate them. This facilitates operations like comparing letters alphabetically.

Unicode is an extended character encoding system that includes a wider range of characters, including those not found in ASCII, such as the letter "ñ" or the character "Č". It ensures backwards compatibility by incorporating the first 127 characters from ASCII.

Computers understand only binary code, where 1 represents electrical current flowing and 0 represents no current. Programmers adapted the representation of data like numbers, letters, and symbols into this binary format.

ASCII uses a table to assign unique numerical values to keyboard symbols. These values allow computers to compare and manipulate characters. For instance, the computer can determine if the letter "a" is greater than the letter "z" based on their assigned numerical values.

Unicode includes a wider range of characters than ASCII. It represents new characters by assigning them unique hexadecimal coordinates. The initial 127 characters in Unicode correspond to the ASCII standard, ensuring compatibility.

Computers can only understand binary code, which uses 1 and 0 to represent information. Since computers need to process various types of information, like numbers, letters, and symbols, programmers developed systems like ASCII and Unicode to assign numerical values to these characters.