Data Representation

What is Data Representation?

• How different types of information (numbers, text, images, sound) are encoded and stored in a computer using binary (0s and 1s).

Components:

Numbers in Binary	Binary System: Base-2 numeral system that uses two digits, 0 and 1. Conversion: Decimal to Binary: Divide the number by 2, record the remainder, and repeat with the quotient until you reach 0. Read the remainders in reverse order. Binary to Decimal: Multiply each binary digit by 2 raised to the power of its position, starting from 0 on the right, and sum the results. Example: Decimal 5 to Binary: $5_{10}=101_2$ Binary 1010 to Decimal: $1\times 2^3+0\times 2^2+1\times 2^1+0\times 2^0=10_{10}$
Text in Binary	Character Encoding: ASCII (American Standard Code for Information Interchange): Uses 7 or 8 bits to represent characters (e.g., 'A' is 65 in decimal or 01000001 in binary). Unicode: Supports a larger set of characters with different encoding forms like UTF-8, which uses 8 to 32 bits. Example: The letter 'A' in ASCII: $01000001$
Images in Binary	Bitmap Images: Pixels: Small dots that make up an image, each pixel is represented by bits. Color Depth: Number of bits used to represent the color of each pixel (e.g., 1-bit for black and white, 24-bit for true color). Vector Images: Description: Represent images using geometric shapes and equations, which are then converted to binary. Example: A 2x2 pixel black and white image: $\begin{array}{cc}0& 1\\ 1& 0\end{array}$ Binary: $01101001$
Sound in Binary	Analog to Digital Conversion (ADC): Sampling: Measuring the amplitude of sound waves at regular intervals. Bit Depth: Number of bits used to represent each sample (e.g., 16-bit, 24-bit). Sampling Rate: Number of samples taken per second (e.g., 44.1 kHz). Example: A sound wave sampled at 44.1 kHz with a bit depth of 16 bits results in a binary representation for each sample.