OCR GCSE Computer Science: Data Representation

OCR GCSE Computer Science: Data Representation

Introduction

Computers operate on a binary system, using only two digits: 0 and 1. Understanding how data is represented in binary is crucial for comprehending how computers process and store information. This tutorial will guide you through the different ways numbers, text, images, and sound are represented in binary.

Number Systems

Binary (Base 2)

• Uses only two digits: 0 and 1.
• Each digit represents a power of 2.

Example:

1011 = (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

Decimal (Base 10)

• The number system we use daily.
• Each digit represents a power of 10.

Example:

123 = (1 * 10^2) + (2 * 10^1) + (3 * 10^0) = 100 + 20 + 3 = 123

Hexadecimal (Base 16)

• Uses digits 0-9 and letters A-F (representing 10-15).
• Each digit represents a power of 16.

Example:

A3 = (10 * 16^1) + (3 * 16^0) = 160 + 3 = 163

Converting Between Number Systems

• Decimal to Binary: Divide the decimal number by 2 repeatedly, noting the remainders. Read the remainders from bottom to top to get the binary equivalent.
• Binary to Decimal: Multiply each binary digit by its corresponding power of 2 and sum the results.
• Decimal to Hexadecimal: Divide the decimal number by 16 repeatedly, noting the remainders. Convert remainders greater than 9 to their corresponding hexadecimal letters.
• Hexadecimal to Decimal: Multiply each hexadecimal digit by its corresponding power of 16 and sum the results.

Text Representation

ASCII (American Standard Code for Information Interchange)

• A standard character set that assigns a unique 7-bit binary code to each character (letters, numbers, punctuation, etc.).
• Allows computers to store and process text.

Example:

A = 01000001

Unicode

• Extends ASCII to support a wider range of characters, including those from different languages and alphabets.
• Uses 16-bit or 32-bit codes.

Example:

é = 00000011 00001101

Image Representation

• Images are represented as a grid of pixels, with each pixel storing color information in binary.
• Color Depth: Determines the number of bits used to represent each pixel's color. Higher color depth means more colors can be displayed.
• Resolution: Represents the number of pixels in an image, affecting its size and detail.

Example:

• A black and white image uses 1 bit per pixel (0 for black, 1 for white).
• A 24-bit color image uses 3 bytes (24 bits) per pixel to represent red, green, and blue components.

Sound Representation

• Sound is represented by digital audio files, where sound waves are sampled at regular intervals.
• Sampling Rate: Determines the number of samples taken per second. Higher sampling rates result in higher fidelity.
• Bit Depth: Determines the number of bits used to represent each sample's amplitude. Higher bit depth means a wider range of sound levels can be captured.

Example:

• A CD-quality audio file uses a sampling rate of 44.1 kHz and a bit depth of 16 bits.

Data Requirements

• Calculating data requirements involves determining the number of bits needed to store a piece of data.
• This can be calculated by considering the data type, its size, and the number of bits used to represent it.

Example:

• A text file with 1000 characters, stored in ASCII, requires 7000 bits (1000 characters * 7 bits/character).

Conclusion

Understanding data representation in binary is essential for anyone studying Computer Science. By learning how different types of data are represented, you gain a deeper insight into how computers process and store information. This knowledge can be applied to various fields, from programming to cybersecurity and data analysis.