Computer Architecture

2.

Data Representation and Computer Arithmetic

2.1.

Information Encoding

2.1.1.

2.1.1.1.

Bits as Fundamental Units

2.1.1.2.

Bytes and Word Sizes

2.1.1.3.

2.1.2.

Character Encoding

2.1.2.1.

2.1.2.2.

Unicode Systems

2.1.2.2.1.

2.1.2.2.2.

UTF-16 Encoding

2.1.2.2.3.

UTF-32 Encoding

2.1.2.3.

Legacy Encodings

2.2.

2.2.1.

Positional Number Systems

2.2.1.1.

2.2.1.2.

Place Value Notation

2.2.2.

Common Number Bases

2.2.2.1.

2.2.2.2.

2.2.2.3.

2.2.2.4.

Hexadecimal System

2.2.3.

Base Conversion

2.2.3.1.

Decimal to Binary

2.2.3.2.

Binary to Decimal

2.2.3.3.

Binary to Hexadecimal

2.2.3.4.

Hexadecimal to Binary

2.2.3.5.

General Conversion Methods

2.3.

Integer Representation

2.3.1.

Unsigned Integers

2.3.1.1.

Representation Method

2.3.1.2.

Range Limitations

2.3.2.

Signed Integer Formats

2.3.2.1.

Sign and Magnitude

2.3.2.1.1.

Representation Structure

2.3.2.1.2.

Range and Limitations

2.3.2.2.

One's Complement

2.3.2.2.1.

Representation Method

2.3.2.2.2.

Arithmetic Properties

2.3.2.3.

Two's Complement

2.3.2.3.1.

Representation Method

2.3.2.3.2.

Advantages and Properties

2.3.2.3.3.

Range Calculation

2.4.

Integer Arithmetic Operations

2.4.1.

Addition and Subtraction

2.4.1.1.

Binary Addition Rules

2.4.1.2.

Binary Subtraction Methods

2.4.1.3.

Carry and Borrow Operations

2.4.2.

Overflow Detection

2.4.2.1.

Overflow Conditions

2.4.2.2.

Detection Methods

2.4.2.3.

Two's Complement Overflow

2.4.3.

Multiplication Algorithms

2.4.3.1.

Basic Binary Multiplication

2.4.3.2.

Sequential Multiplier Design

2.4.3.3.

Booth's Algorithm

2.4.3.3.1.

Algorithm Steps

2.4.3.3.2.

Signed Number Handling

2.4.4.

Division Algorithms

2.4.4.1.

Basic Binary Division

2.4.4.2.

Restoring Division

2.4.4.3.

Non-Restoring Division

2.5.

Floating-Point Representation

2.5.1.

Scientific Notation Concepts

2.5.1.1.

2.5.1.2.

Exponent and Mantissa

2.5.2.

IEEE 754 Standard

2.5.2.1.

Standard Overview

2.5.2.2.

Format Components

2.5.2.2.1.

2.5.2.2.2.

2.5.2.2.3.

2.5.2.3.

Precision Formats

2.5.2.3.1.

Single Precision

2.5.2.3.2.

Double Precision

2.5.2.3.3.

Extended Precision

2.5.3.

2.5.3.1.

2.5.3.2.

Positive and Negative Infinity

2.5.3.3.

Denormalized Numbers

2.5.3.4.

Zero Representations

2.6.

Floating-Point Arithmetic

2.6.1.

Addition and Subtraction

2.6.1.1.

Exponent Alignment

2.6.1.2.

Mantissa Operations

2.6.1.3.

2.6.2.

Multiplication and Division

2.6.2.1.

Exponent Arithmetic

2.6.2.2.

Mantissa Operations

2.6.3.

Rounding Methods

2.6.3.1.

Round to Nearest

2.6.3.2.

Round Toward Zero

2.6.3.3.

Round Toward Positive Infinity

2.6.3.4.

Round Toward Negative Infinity

2.6.4.

Exception Handling

2.6.4.1.

Overflow Conditions

2.6.4.2.

Underflow Conditions

2.6.4.3.

Inexact Results

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3. Instruction Set Architecture