Unit III: Hardware

Main Units of a Computer

A physical computer system consists of four main functional units working together:

Processor (CPU) — interprets and executes instructions. It contains:

• Control Unit — acts like a traffic controller, directing the flow of data and instructions throughout the CPU and coordinating operations.
• Arithmetic and Logic Unit (ALU) — performs all arithmetic calculations (addition, subtraction, etc.) and logical comparisons (AND, OR, NOT, etc.).
• Registers — tiny, high-speed storage locations inside the processor that temporarily hold data and instructions currently being processed.
• System Clock — generates regular electronic pulses (ticks) that set the operating pace for all components in the system unit.

Main Storage (Memory) — holds the data and instructions currently in use. Memory stores three types of content: the operating system and system software, application programs, and the data being processed.

Types of memory:

• RAM (Random Access Memory) — stores data and instructions currently in use; volatile (contents are lost when power is removed).
• Cache Memory — a small, very fast holding area for data the CPU uses frequently, reducing the time needed to fetch it from regular RAM.
• ROM (Read-Only Memory) — contains the basic instructions a computer needs to start up; non-volatile (retained without power).
• CMOS — stores configuration information (RAM capacity, date/time, drive types) that is read every time the computer is powered on.

Input Devices — hardware used to send data into a computer. Examples: keyboard, mouse, scanner, optical mark reader, touch screen, light pen, microphone, MICR (Magnetic Ink Character Recognition) readers used for processing bank checks.

Output Devices — hardware used to send processed data out from the computer. Examples: monitor, printer, speakers, projector.

Secondary (Auxiliary) Storage

Secondary storage holds data permanently, outside of the main memory. It exists because RAM can only hold limited data and loses everything when power is cut.

Types of secondary storage:

• Magnetic tape — serial access; data can only be read in order; high capacity; inexpensive.
• Magnetic disk — direct access; data can be read from any location quickly; uses electromagnetic read/write heads.
• Optical disc (CD, DVD, Blu-ray) — reads and writes data using laser beams.
• Solid State Drive (SSD) — uses integrated circuit assemblies with no moving parts; faster and more durable than magnetic disks.
• Flash drives and external drives — portable storage.
• Cloud storage — data stored on remote servers accessible over the internet.

Boolean Algebra

George Boole (1815–1864) developed an algebraic system for handling logical statements, now called Boolean algebra. Claude Shannon (1916–2001) later showed in 1938 that Boolean algebra could be applied directly to electronic switching circuits, which became the foundation of digital circuit design.

Boolean algebra differs from ordinary algebra in key ways:

• It deals with only two values: 0 (false) and 1 (true).
• It includes a complement operation (NOT) that has no equivalent in ordinary algebra.
• There is no subtraction or division.

The three fundamental operations are:

Truth table for basic operations:

NOT:   0' = 1,  1' = 0

AND:   0•0=0,  0•1=0,  1•0=0,  1•1=1

OR:    0+0=0,  0+1=1,  1+0=1,  1+1=1

Logic Gates

Logic circuits are often called gates. Each gate takes one or more binary input signals and produces a single binary output.

NOT Gate (Inverter): Flips the input. Input A → Output A'

AND Gate: Output is 1 only when ALL inputs are 1.

OR Gate: Output is 1 when AT LEAST ONE input is 1.

NAND Gate: AND followed by NOT. Output is 0 only when all inputs are 1 (the inverse of AND). NAND is a universal gate — any other gate can be built from NAND gates alone.

NOR Gate: OR followed by NOT. Output is 1 only when all inputs are 0 (the inverse of OR). NOR is also a universal gate.

XOR Gate (Exclusive OR): Output is 1 when inputs are different. If inputs are the same, output is 0.

XNOR Gate (Exclusive NOR): The inverse of XOR. Output is 1 when inputs are the same.

Using universal gates reduces the variety of physical gates needed in manufacturing and simplifies circuit fabrication.

Boolean Postulates and Theorems

Key identities for simplifying Boolean expressions:

Example simplification using Distributive and Complement:

F = AB + BC + B'C
  = AB + C(B + B')    ← factor out C
  = AB + C            ← because B + B' = 1

De Morgan's Theorems

Two essential rules for converting between AND and OR forms:

Theorem 1: (X + Y)' = X'Y' → A NOR gate is equivalent to a bubbled AND gate (AND with inverted inputs)

Theorem 2: (XY)' = X' + Y' → A NAND gate is equivalent to a bubbled OR gate (OR with inverted inputs)

Double inversion has no effect: inverting a signal twice returns it to its original state. This principle is used to convert circuits between equivalent forms without changing logical behavior.