Assignment 1: The Devil is in the
Data
Introduction
Unit 19: Computer Systems Architecture
Learning Aims: P1, P2, P3, P4, M1
Understanding Data
Representation
- Numeric and alphanumeric data coding in computer systems (P1)
- Explanation: Data in computer systems is represented using various codes that enable computers to
process and store information. Numeric data involves using symbols to represent numbers, while
alphanumeric data includes letters, numbers, and special characters.
- Example: In ASCII encoding, each character is represented by a numeric code. For instance, the
letter 'A' is represented by the ASCII code 65.
Number Systems Overview
- Decimal, binary, octal, and hexadecimal number systems
- Importance of various number systems in computer architecture
- Explanation: Different number systems provide alternate ways to represent numbers. Decimal is common for human use, binary is
essential for computing, octal and hexadecimal are used for compact representation and ease of conversion.
- Example: The binary system is fundamental to computers. Computers use binary digits (bits) to perform calculations and store
data. A bit can represent either a 0 or a 1, which aligns with the electronic on/off states of computer circuits.
Converting Between Number
Systems: Example
- Example: Convert denary 35 to binary and then to hexadecimal
- Explanation: Converting between number systems involves changing the base of a number while
preserving its value. Start by converting to binary and then to hexadecimal.
- Example: Denary 35 ? Binary 00100011 ? Hexadecimal 23
- Explanation: 35 in denary is 00100011 in binary. Splitting into nibbles, 0010 corresponds to Hex 2,
and 0011 corresponds to Hex 3. Combined, 35 (denary) is 23 (hexadecimal).
ASCII Encoding and Character
Storage
- ASCII table and character encoding (P1)
- Explanation: ASCII assigns numeric codes to characters for storage and
communication in computers.
- Example: The character 'H' is represented by ASCII code 72, 'e' by 101, and 'l'
by 108.
Digital Encoding of Sound
- Sound representation in digital form (P2)
- Explanation: Sound waves are converted into digital form through sampling and
quantization. Each sample represents the sound wave's amplitude at a specific point in
time.
- Example: In audio CDs, sound is sampled at 44,100 times per second. Each sample is
quantized to a specific digital value, preserving the sound's characteristics.
Digital Encoding of Images
- Bitmap graphics representation (P2)
- Explanation: Images are divided into pixels, each pixel storing color
information. Bitmap graphics use binary codes to represent pixel colors.
- Example: A black-and-white image is often stored using one bit per pixel,
where 0 represents black and 1 represents white.
Converting Numeric Data:
Examples
- Examples of converting denary, binary, and hexadecimal
- Example 1: Converting denary 123 to binary ? Binary 1111011
- Example 2: Converting binary 110110 to denary ? Denary 54
- Example 3: Converting binary 101101 to hexadecimal ? Hexadecimal 1B
- Example 4: Converting denary 252 to hexadecimal ? Hexadecimal FC
Floating Point Representation
- Understanding and working with 32-bit floating point format (P3)
- Explanation: Floating-point representation allows expressing real numbers with
great range and precision. It consists of a sign bit, exponent, and fraction.
- Example: In 32-bit floating point, a number might be represented as 0 10010110
11011000100000000000000, where the sign is positive, exponent is 38, and fraction
represents the decimal part.
Boolean Logic and Logic Gates
(Optional)
- Brief introduction to basic Boolean logic (P4)
- Explanation: Boolean logic involves true/false values combined using logical
operators (AND, OR, NOT). Logic gates implement these operations in
hardware.
- Example: An AND gate outputs true only when both inputs are true.