COMP-1200 Spring 2025 Notes

Course Overview

Institution: Wentworth Institute of Technology
Presented by: Prof. Gyllinsky
Based on slides by: Prof. Park, Prof. Firouzbakht, Prof. Anwaruddinta

Binary Arithmetic

Subtraction in Binary (8-bit signed numbers):
Binary arithmetic is crucial in computer science, particularly in the context of representing signed numbers. In an 8-bit binary system, numbers are represented using two's complement notation, where the highest bit indicates the sign of the number.
Example: $0110 1101 - 0001 1000$
This operation involves borrowing, similar to decimal subtraction, as well as consideration for potential overflow in signed binary numbers, which occurs if the result exceeds the representable range of values.
Possible answers:
A. Overflow, 0x55
B. No overflow, 0x55
C. Overflow, 0x65
D. No overflow, 0x65

Digital Symbols

Digital symbols correspond to analog voltages:
Understanding the relationship between digital signals and analog voltages is fundamental in electronics and computer engineering.
"0" = 0V
"1" = 3V
These two levels of voltage define a binary system that allows for the representation of data and instructions in digital devices. Additionally, it is important to note that "illegal" states can occur if the voltage is outside the defined range, which can lead to incorrect operations in logic circuits.

Switch-based Circuits

Representation of States:
In digital circuits, two primary states are utilized: On/Off, Open/Closed, Voltage/No Voltage.
Simple Switch Circuit:
Switch Open (Off):

• No current flows through the circuit: Light stays off, and the output voltage ($V_{out}$) is +2.9V.
  Switch Closed (On):

• Current flows through the circuit, allowing the light to turn on, resulting in an output voltage ($V_{out}$) of 0V.
  This illustrates the basic operational principles behind common electronic switches and their influence on circuit behavior.

Transistors

Definition:
A transistor is a fundamental building block in digital logic systems, acting as a switch or amplifier for electrical signals. Transistors can control the flow of current in circuits and are key to constructing logic gates.

Historical Context:

• Intel 4004 (1971): 2300 transistors

• Intel Pentium 4 (2000): 48 million transistors

• Intel Sandy Bridge (2011): 1 billion transistors

• Apple M1 (2021): 16 billion transistors
  These advances demonstrate the exponential growth in integration density and performance of microprocessors over time, exemplifying technological progress in the semiconductor industry.

Moore's Law

Concept:
Moore's Law states that the number of transistors on a microprocessor chip doubles approximately every two years, a prediction made by Gordon Moore in 1965. This concept has fundamental implications for performance and efficiency in computing, influencing tech development and market strategies across many sectors.

MOSFET Transistors

Types:
Two types are n-type and p-type, each serving different functions in circuit design.
n-type MOSFET:

• Gate voltage positive => closed circuit between terminals, allowing current to flow.

• Gate voltage zero => open circuit, stopping current.

• Terminal #2 connected to Ground (0V).

p-type MOSFET:

• Gate voltage positive => open circuit, preventing current flow.

• Gate voltage zero => closed circuit, allowing current to flow.

• Terminal #1 connected to +2.9V.
  Understanding these components is vital for designing efficient power and logic circuits in various digital applications.

Basic Logic Gates

NOT Gate (Inverter):

• Input/Output behavior:
  If Input = 0, Output = 1
  If Input = 1, Output = 0
  This gate is fundamental in digital logic for inverting signals.

AND Gate:

• Output = 1 only if all inputs are 1.
  This gate is used for implementing logic functions that require multiple true conditions.

OR Gate:

• Output = 1 if at least one input is 1.
  This gate is crucial in circuits where a single true condition meets the requirements.

Combining Logic Gates

NAND Gate:

• Result is negation of AND operation; a vital building block in digital circuit design, often leading to higher-performance designs.

NOR Gate:

• Result is negation of OR operation, also frequently used in constructing various logical functions through combinations.

Logic Circuits

Combinational Logic Circuit:

• Output depends only on current inputs.
  These circuits perform specific operations based solely on input conditions, with no memory.

Sequential Logic Circuit:

• Output depends on the sequence of inputs; can remember past inputs.
  They incorporate memory elements to retain state information, allowing for more complex operations in digital designs.

Future Topics

Upcoming topics to explore:

• Information Representation, vital for understanding how data is formatted and stored.

• Digital Logic Systems, focusing on how to analyze and design complex logic circuits.

• Combinational Logic, where modules are assembled to perform versatile functions in computational tasks.