[Recover Note] For Computer Organisation Quiz 2

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Lecture 4: From Transistors to Gates

1. Key Historical Figure: Claude Shannon

• Master’s Thesis (1937): Shannon proposed that electrical switches can perform Boolean logic, which was revolutionary for computing. His work is considered one of the most important master’s theses in history.

2. From Switches to Boolean Logic

• Switch States:
• Open = 0 (False)
• Closed = 1 (True)
• Relays and Vacuum Tubes: Earlier technologies used to create circuits before transistors.
• Transistors: Tiny, cheap, and reliable electronic components that function like switches, replacing relays and vacuum tubes.

3. Transistor Basics

• Definition: A transistor controls the flow of electrical signals by acting as a switch.
• Water Flow Example:
• Gate on (transistor conducts) = water flows (1)
• Gate off (transistor blocks) = water stops (0)
• Types:
• N-type: Conducts when the gate-source voltage (V_GS) is high.
• P-type: Conducts when the gate-source voltage (V_GS) is low.

4. CMOS Transistors

• Complementary Metal-Oxide-Semiconductor (CMOS): Combines both P-type and N-type transistors.
• N-type: Closed (conducting) when gate is on (1), open (insulating) when gate is off (0).
• P-type: Open (insulating) when gate is on (1), closed (conducting) when gate is off (0).

5. From Transistors to Logic Gates

• Logic Gates: Devices that perform Boolean functions based on input values. Gates are built using transistors.
• Basic Logic Gates: NOT, OR/NOR, AND/NAND, XOR.
• Transistors per Gate: Typically, 1 to 6 transistors are used to construct a gate.

6. Common Logic Gates

• NOT Gate (Inverter):
• Input 0 produces output 1.
• NOR Gate:
• Output is true only when both inputs are false.
• AND/NAND Gates:
• AND: Both inputs must be true for the output to be true.
• NAND: Produces the opposite result of AND.

7. Universal Logical Gates

• Universal Gate: Can implement any Boolean function without the need for other types of gates.
• NAND Gate: A universal gate that can be used to build any other gate.
• NOR Gate: Another universal gate that functions similarly.

8. Key Concepts

• Information Representation: Information can be represented by bits.
• Binary Arithmetic: Boolean algebra allows binary operations.
• Shannon’s Contribution: Boolean logic can be realized with electrical switches.
• Transistors: Essential components that switch electronic signals.
• NAND/NOR Gates: Both are universal gates, crucial in designing integrated circuits.

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Lecture 5: From Gates to Circuits I: Combinational Circuits

1. From Gates to Circuits

• Logic Gates: Small electronic devices that compute functions using two-valued signals (0, 1).
• Boolean Functions: Can be represented in three forms:
• Truth Table
• Logic Expression
• Logic Circuit

2. Logic Circuits

• Definition: A collection of gates connected together to implement Boolean functions.
• Integrated Circuits (ICs): Tiny transistors integrated into a small chip, which are foundational to modern digital logic circuits.

3. Two Types of Circuits

• Combinational Logic Circuits:
• Output depends solely on the current input.
• No memory, “memoryless.”
• Sequential Logic Circuits:
• Output depends on both the current input and the current state (which stores previous input).
• Contains memory.

4. Combinational Circuits

• Key Features:
• No memory, multiple inputs, and multiple outputs.
• Each output is determined by a Boolean function.
• Described by:
  • n-input, m-output truth tables.
  • Logic diagrams.

5. Binary Addition Circuits

• Half Adder:
• Adds two single bits.
• Produces a sum (s) and a carry bit (c).
• Logic expressions and circuit diagrams are used to implement this function.
• Full Adder:
• Adds three bits (A, B, and Carry-in).
• Outputs a sum and a carry-out.
• 4-bit Adder (Ripple-Carry Adder):
• A series of full adders can be used to add two 4-bit numbers.
• The carry-out of one adder feeds into the carry-in of the next adder.
• Slow in performance due to sequential carry propagation (ripple effect).

6. Decoder

• Definition: Selects one specific output from a set of inputs.
• Usage: Commonly used to decode memory addresses in a computer.
• For example, a 2-4 Decoder decodes 2 input bits into 4 possible output lines, where only one line is active (set to 1) at a time.

7. Multiplexer

• Definition: Selects a single output from multiple inputs.
• Control Lines: The specific input chosen for output is determined by the values on control lines.
• A 4-to-1 Multiplexer selects one input out of four based on two control lines (log₂ 4 = 2).

8. Combinational Circuit Analysis

• Analyze circuits by identifying the logic function that they implement using a combination of truth tables, Boolean expressions, and logic diagrams.

9. Combinational Circuit Design Process

• Steps:

1. From the design specification, create a truth table.
2. Derive the Boolean expression in Sum of Products (SOP) or Product of Sums (POS) form.
3. Use a Karnaugh Map to simplify the Boolean expression.
4. Implement the simplified expression using logic gates.
5. Verify the result.

10. Example: Comparator Circuit Design

• Design a circuit that compares two 1-bit numbers (A and B). The outputs are:
• G (Greater): 1 if A > B.
• E (Equal): 1 if A = B.
• L (Lesser): 1 if A < B.
• The circuit design involves filling in a truth table, deriving the logic expressions, and simplifying them.

Key Concepts to Remember

• Combinational Circuits:
• No memory.
• Basic building blocks for more complex systems.
• Examples: Half adder, full adder, decoder, multiplexer, ALU.
• Design and Analysis: Understand how to go from truth tables to Boolean expressions and simplified logic gate diagrams.

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Lecture 6: From Gates to Circuits II: Sequential Circuits

1. Sequential Circuits Overview

• Difference from Combinational Circuits:
• Combinational Circuits: Output depends solely on current inputs (memoryless).
• Sequential Circuits: Output depends on current inputs and previous inputs (current state), meaning they have memory.

2. Memory in Sequential Circuits

• Definition: Memory allows circuits to “hold” or “remember” a value.
• Write: You can change the stored value.
• Hold: The value can be retained.
• Read: The stored value can be retrieved.
• One-Bit Memory:
• A basic unit capable of holding a single bit (0 or 1).
• It can be set (1) or reset (0).

3. Feedback in Circuits

• Feedback: The output of a circuit is fed back into the circuit as input. This feedback mechanism is essential for memory in sequential circuits.

4. SR Latch (Set-Reset Latch)

• Building Block: A fundamental unit in sequential circuits, analogous to gates in combinational circuits.
• Characteristic Table:
• SR = 00: Stores the previous value.
• SR = 01: Resets to 0.
• SR = 10: Sets to 1.
• SR = 11: Undefined (unstable).
• Gated SR Latch: Adds an enable input (EN) to control when the latch can change state.
• SR-NAND Latch: A variation of the SR latch using NAND gates.

5. Clocking and Timing

• Gate Delay: The small time delay between input changes and output changes, called gate delay, can cause glitches.
• Clock: A clock circuit produces electrical pulses that control when the state of the circuit can change.
• Clock Speed: Measured in MHz (millions of pulses per second).
• Edge-Triggered: Changes states on the rising or falling edge of the clock signal.
• Level-Triggered: Changes states whenever the clock signal is high or low.
• Latches vs. Flip-Flops:
• Latch: Level-triggered.
• Flip-Flop: Edge-triggered.

6. JK Flip-Flop

• JK Flip-Flop: A modified SR flip-flop that eliminates the undefined state by using feedback. Only one input (Set or Reset) is active at a time, preventing illegal states.

7. D Flip-Flop (Data Flip-Flop)

• Simplified Circuit: Stores one bit of data.
• Operation: When the clock signal is high, whatever is on the D (data) input is stored in the Q (output).
• Use: A true representation of physical computer memory.

8. Registers and Binary Counters

• Register:
• A group of flip-flops that can store multiple bits (e.g., 4-bit register).
• Includes additional lines for power, ground, and a clear/reset line.
• Write Enable (WE): Allows data to be written into the register.
• Binary Counter:
• A sequential circuit that outputs binary numbers in sequence (e.g., from 0000 to 1111).
• Implemented using a series of JK flip-flops.

9. Memory Design and Addressing

• 4×3 Memory Example: Represents a simple memory where each column holds a 3-bit word.
• Decoder: Selects the correct memory location based on input addresses.
• Memory Addressing: For a simple microprocessor with 1KB memory (10 address lines), memory chips are selected and addressed using decoders and specific lines (e.g., 128×8 memory chips).

10. 7-Segment Display

• Truth Table: Used to display numbers (0-9) on a 7-segment display.
• Design Question: How to display numbers from 0 to 9 sequentially?

Key Concepts to Remember

• Sequential Circuits: Can remember previous inputs due to feedback and memory elements.
• Flip-Flops: Key memory elements in sequential circuits (SR, JK, D flip-flops).
• Clocking: Clocks are used to control when sequential circuits update their states.
• Registers and Counters: Built using flip-flops to store and process multiple bits of data.
• Memory: Involves addressing and decoding circuits to read and write data efficiently.