Data Representation – in Computer Architecture

What You’ll Learn 📚

• Core concepts of data representation
• Key terminology and definitions
• Simple to complex examples
• Common questions and answers
• Troubleshooting common issues

Introduction to Data Representation

At its core, data representation is about how computers understand and manipulate data. Computers use binary (0s and 1s) to represent all types of data, whether it’s numbers, text, images, or sounds. But how does this work? 🤔 Let’s break it down!

Core Concepts

Computers use a binary system because it’s simple and reliable. Each binary digit (bit) can be either a 0 or a 1. By combining multiple bits, computers can represent larger numbers and more complex data.

Key Terminology

• Bit: The smallest unit of data in a computer, representing a binary value (0 or 1).
• Byte: A group of 8 bits, which can represent 256 different values (2^8).
• Binary System: A base-2 numeral system used by computers, consisting of only 0s and 1s.
• Hexadecimal: A base-16 numeral system, often used as a human-friendly representation of binary-coded values.

Simple Example: Binary Representation of Numbers

# Simple binary representation example
def binary_representation(number):
    return bin(number)

# Convert the number 5 to binary
print(binary_representation(5))

Progressively Complex Examples

Example 1: Binary Addition

# Binary addition example
def binary_addition(a, b):
    return bin(int(a, 2) + int(b, 2))

# Add binary numbers '101' (5) and '110' (6)
print(binary_addition('101', '110'))

Example 2: Hexadecimal Representation

# Hexadecimal representation example
def hex_representation(number):
    return hex(number)

# Convert the number 255 to hexadecimal
print(hex_representation(255))

Example 3: Text Representation (ASCII)

# ASCII representation example
def ascii_representation(character):
    return ord(character)

# Get ASCII value of 'A'
print(ascii_representation('A'))

Common Questions and Answers

1. Why do computers use binary?

   Computers use binary because it’s simple and reliable. Binary only has two states (0 and 1), which can be easily represented with electrical signals.

2. What is the difference between binary and hexadecimal?

   Binary is a base-2 system using only 0s and 1s, while hexadecimal is a base-16 system using digits 0-9 and letters A-F. Hexadecimal is often used because it’s more compact and easier for humans to read.

3. How do I convert binary to decimal?

   To convert binary to decimal, multiply each bit by 2 raised to the power of its position from right to left, starting at 0, and sum the results.

4. What is ASCII?

   ASCII (American Standard Code for Information Interchange) is a character encoding standard that uses numbers to represent characters. For example, ‘A’ is represented by 65.

Troubleshooting Common Issues

If you’re getting unexpected results, double-check your binary or hexadecimal inputs. Even a small mistake can lead to incorrect outputs.

Remember, practice makes perfect! Try converting numbers between binary, decimal, and hexadecimal to get comfortable with these systems.

Practice Exercises

• Convert the decimal number 42 to binary and hexadecimal.
• Add the binary numbers ‘111’ and ‘101’.
• Find the ASCII value of the character ‘Z’.

Keep practicing, and don’t hesitate to revisit this guide whenever you need a refresher. You’ve got this! 💪

For more information, check out the Wikipedia page on binary numbers and the Wikipedia page on ASCII.