6.0 Data Representation - Characters and Boolean

Tags: #◇Computer Science #◇CCICOMP #◇Problem Solving #◇M2

---

◇Overview

Since computers process only bits, character and boolean data cannot be represented directly. Characters are represented indirectly by mapping them to numeric values via standard coding tables, balancing compactness with representational range. Standard methods include ASCII and Unicode. Boolean data, consisting solely of true or false values, conceptually requires only a single bit, but CPU designers often use integer formats where $0$ corresponds to false and any non-zero value corresponds to true. Operations on booleans rely on logic gates, extending naturally to bitwise operations that manipulate entire bit strings simultaneously.

◇Key Definitions

Character Encodings ASCII (American Standard Code for Information Interchange): A standard $7$-bit (or $8$-bit) encoding format supporting at least $128$ characters, commonly used in early and modern systems for English and basic symbols. Unicode: A newer $16$-bit or $32$-bit encoding standard designed to support a vast array of international characters. ASCII is a subset of Unicode. Strings: Complex data types composed of sequential series of character codes. Device Control Codes: Non-printable characters (e.g., Carriage Return CR, Line Feed LF) used for formatting text when communicating with output devices.

Boolean Operations & Logic Gates NOT (Inverter): $Y = A'$. Negates the input. Output is $1$ if input is $0$, and vice-versa. AND: $Y = AB$. Outputs true ($1$) only if all inputs are true. OR: $Y = A + B$. Outputs true ($1$) if at least one input is true. XOR (Exclusive-OR): $Y = A \oplus B$ or $Y = A'B + AB'$. Outputs true ($1$) if the inputs differ (an odd number of $1$s).

◇Worked Examples

1. ASCII String Interpretation

Given the hexadecimal value $434349434\text{F}4\text{D}50$, what is the ASCII interpretation?
By parsing every two hex digits: $43\text{h} \to \text{'C'}$ $43\text{h} \to \text{'C'}$ $49\text{h} \to \text{'I'}$ $43\text{h} \to \text{'C'}$ $4\text{F}\text{h} \to \text{'O'}$ $4\text{D}\text{h} \to \text{'M'}$ $50\text{h} \to \text{'P'}$
Result: "CCICOMP"

2. Bitwise Logic Operations Bitwise NOT: $\text{NOT } \text{F}3\text{h} \implies \text{NOT } 11110011_2 = 00001100_2 = 0\text{C}\text{h}$ Bitwise AND: $23\text{h} \text{ AND } 01\text{h}$ (Masking to check if a number is odd)

$23\text{h} = 00100011_2$
$01\text{h} = 00000001_2$
Result: $00000001_2 \implies$ Odd (true) Bitwise OR: $11110011_2 \text{ OR } 10000101_2 = 11110111_2$ Bitwise XOR: $11110011_2 \text{ XOR } 10000101_2 = 01110110_2$

3. Boolean Functions

A single-bit adder can be described by boolean functions: Sum: $Y = A'B + AB'$ ($A \text{ XOR } B$) Carry: $C = AB$ ($A \text{ AND } B$)

◇References & Navigation

• Previous Topic: ◇Data Representation - Real Numbers
• Next Topic: ◇Arithmetic Operations in Binary
• Related Notes: ◇Data Representation - Integers, ◇Boolean Algebra