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How to Build a Computer

This book goes from electrical signal → computer:

  1. Signals
  2. Switches
  3. Logic Gates
  4. Combinational Circuits
  5. Clocks and Oscillators
  6. Memory (Flip-Flops and Latches)
  7. CPU
  8. Instruction cycle
  9. Stored programs

1. Signals

How do you represent information physically?

A signal is a physical quantity used to represent information.

  • Typically voltage levels in a wire
  • Two stable regions are interpreted as:
    • Low → 0
    • High → 1
  • Meaning is assigned externally (not intrinsic)

Other signals:

  • Light pulses
  • EM wave pulses
  • Smoke signals

2. Switches

How do we control whether electrons can move from A to B?

  • Mechanical → physically block path
  • Vacuum tube → allow/block in empty space (1900s)
  • Transistor → reshape material so path exists or not (1940s)

Transistor Basics

A transistor is a voltage-controlled switch.

  • With no voltage on the gate → no conductive path → OFF
  • Apply sufficient voltage to the gate → the electrical field pull electrons in the semiconductor to create a conductive channel → ON
  • The gate does not carry the main current; it controls flow between source and drain

Gate Voltage = 0V

Gate Voltage < Terminal Voltage

Gate Voltage Greater than Terminal Voltage

3. Logic Gates

How do we build decision-making from switches?

A logic gate is a circuit that gives different outputs based on the inputs.

Built from transistors arranged in a certain way so that voltage patterns implement rules of logic.

  • Transistor = switch
  • Gates = networks of switches
  • Output depends only on current inputs

Logic gates are all connected to ground and a voltage source. The inputs enabling/disabling the flow from source to ground. Which is why a NOT gate can have a voltage output with no input (the input disables the flow).

3.1. AND

3.2. OR

3.3. NOT

These three are functionally complete → all computation can be built from them.

4. Combinational Circuits

How do we combine gates into useful operations?

Combinational circuits are logic systems with:

  • No memory
  • Output depends only on current inputs

4.1. Half Adder

Adds two bits:

  • Sum = XOR(A, B)
  • Carry = AND(A, B)

4.2. Full Adder

Combines two half adders:

4.3. 8-bit Adder

Combines 8 full adders (uses 2s complement for subtraction):

ABOverflowOutcome
++0No error
++1Error (sum too large)
+-0No error
+-1No error
-+0No error
-+1No error
--0No error
--1Error (difference too small)

4.4. 8-bit Accumulating Adder

  • Initially flip flops store 0.
  • Flip flop output is routed to the full 8-bit adder input.
  • The 8-bit input is the second input into the full 8-bit adder.
  • The result of the full 8-bit adder is stored in the flip flops.
  • The “add” is likely triggered by a clock cycle.

5. Clocks and Oscillators

How do we coordinate time in hardware?

A clock is a repeating electrical signal:

  • 0 → 1 → 0 → 1 …

Without timing → circuits change unpredictably as switching components on/off is not synchronised

With clock → all components update in sync

5.1. Crystal Oscillator

A current applied to the crystal (quartz) causes it to vibrate at a certain fixed frequency (dependant on size/shape etc).

5.2. Oscillating Relay

A relay connected to itself causes it to switch itself on/off at a certain frequency (dependant on the length of metal switch)

6. Memory (Flip-Flops & Latches)

How do we store a bit?

6.1. Latch

Level-sensitive (state changes when clock is on)

6.1.1. Level-triggered D-type Latch

6.1.2. Level-triggered D-type Latch with Clear

6.2. Flip-flop

Edge-triggered (state changes only on clock rise/fall)

6.2.1. Edge-Triggered D-Type Flip-Flop with Clear and Preset

6.2.2. Edge-Triggered D-Type Flip-Flop with Clear and Preset

6.3. Binary Clock/Counter

If you connect a flip flop to an oscillator, the flip flop switches at half the frequency. Connecting multiple flip flops creates a binary clock. As each one oscillates at half the frequency of the previous one.

7. CPU (From Parts to System)

How do we combine memory and logic into a machine that can execute instructions?

A CPU is built from:

  • Registers (small fast memory)
  • ALU (calculation unit)
  • Control Unit (decision logic)
  • Buses (communication)

7.1 Registers

Where does the CPU store values it is actively working on?

A register is:

  • A group of flip-flops (8 bit register shown below)
  • Stores a fixed number of bits (e.g. 8-bit, 16-bit)

Types of Registers

7.1.1. General Purpose Registers

  • Used for temporary values
  • There are normally 5-10 of these
  • Example:
    • Store numbers for calculations
    • Hold intermediate results

7.1.2. Special Purpose Registers

  • Program Counter (PC)
    • Holds address of next instruction
  • Instruction Register (IR)
    • Holds current instruction being executed
  • Accumulator (ACC)
    • Stores results of ALU operations
  • Memory Address Register (MAR)
    • Holds address for memory access
  • Memory Data Register (MDR)
    • Holds data being read/written

7.2 ALU (Arithmetic Logic Unit)

How does the computer actually compute?

The ALU is a combinational circuit (no storage) that performs arithmetic and logic operations:

  • Addition
  • Subtraction (2’s complement)
  • Bitwise logic (AND, OR, NOT, XOR, shifting etc.)

How it Works

  • A - input into ALU
  • B - attached to accumulator register
  • F2, F1, F0 - control bits that activate the circuitry to perform a specific function
  • Flags - indicators raised on the current operation

Add/Sub Module

Logic Module

7.3 Buses

How do all components share data?

A bus is a shared set of wires between components. It can only be in use by one component at a time otherwise it will short circuit or produce garbage output.

Types of Buses

  • Data Bus → carries actual values
  • Address Bus → selects location
  • Control Bus → carries signals (read/write, enable, clock)

7.4 Tri-State Buffers

How do we prevent components from “talking over each other” on the buses?

A tri-state buffer has 3 states:

  • 0 → drives line low
  • 1 → drives line high
  • High impedance (Z) → disconnected

This allows:

  • Only one component to drive the bus at a time, others remain electrically invisible
  • When components are “enabled”, they are connected to the buses.
  • Once the CU decodes an instruction, it enables/disables components to connect them to the buses.

7.5 RAM (Main Memory)

Where are programs and data stored long-term (during execution)?

RAM is:

  • A large array of flip flops (16 x 8 bit flip flops in image below)
  • Each byte is indexed by an address (4 bit address below)
  • The address enables a row/column in the array
  • Once enabled, the output of RAM is set to the contents at the address
  • If written to, it changes the content at that address
  • An address refers to one 8-bit location (1 byte)

7.6 Control Unit (CU)

What tells everything when to act?

The Control Unit contains the following subcomponents:

  • Instruction latches
  • Instruction decoder
  • Program counter

What it Does

  • Reads instruction from RAM into instruction registers
  • Decodes opcode (by responding to bit patterns in the opcode itself)
  • Enables/disables parts of the CPU through control signals:
    • Registers (load/clear)
    • ALU operation selection
    • Memory read/write
    • Bus access (via tri-state buffers)

No intelligence. Just:

  • If opcode = 0001 ADD control signal is active
  • If opcode = 0010 LOAD control signal is active

8. Instruction Cycle

How does the whole system actually run?

Repeating process:

1. Fetch

  • The PC (program counter) is enabled onto the address bus
  • RAM (memory) is enabled on the data bus, the opcode at that address is returned
  • The IR (instruction register) is enabled on the data bus and the opcode is stored in the IR

2. Decode

  • CU interprets opcode (by responding to bit patterns in the opcode itself)

3. Execute

  • CU activates:
    • Registers
    • ALU
    • Memory
    • Buses

4. Update

  • Result stored in RAM
  • PC incremented

9. Stored Programs

What makes this a general-purpose computer?

Instructions are stored in RAM just like data.

So:

  • Data = numbers
  • Instructions = also numbers

This allows:

  • Programs to be loaded, changed, reused
  • Same hardware → many different behaviors

9.1 Machine Code

What does the CPU actually understand?

The CPU only understands binary instructions:

  • Example:
    • 0001 0010 → might mean “ADD register A and B”
    • 0010 0100 → might mean “LOAD from memory”

These are called machine code instructions:

  • Each instruction = opcode + operands
  • Interpreted directly by the Control Unit

This is the real language of the machine.

9.2 Assembly Language

How do humans work with machine instructions?

Assembly is a human-readable version of machine code.

Instead of:

0001 0010

We write:

ADD A, B

Key points:

  • One-to-one mapping with machine code
  • Still very close to hardware
  • Uses symbolic names for:
    • Instructions
    • Registers
    • Memory addresses

An assembler converts:

Assembly → Machine code

9.3 High-Level Languages

How do we write complex programs efficiently?

High-level languages (e.g. Python, C, Java) are:

  • More abstract
  • Closer to human thinking
  • Independent of specific hardware

Example:

x = a + b

This gets translated into many assembly instructions.

9.4 Compilers

How do high-level programs become machine code?

A compiler translates:

High-level language → Machine code

Steps (simplified):

  1. Parse code (understand structure)
  2. Optimise (improve efficiency)
  3. Generate assembly/machine code

Some languages use:

  • Interpreter → runs code line-by-line
  • Compiler → produces executable file

Charles Petzold

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