Number Representations

• Number Representations
• Binary Representation of Information
• Converting between decimal and binary
• BINARY, OCTAL and HEXADECIMAL NUMBERS
• EXAMPLES
• Binary representation of signed integers
• Binary representation of everything else
• ASCII Conversion Table
• Connection to the world of hardware
• Tutorial
• Number System Conversion Tool

Binary Addition and Subtraction

• Binary Addition
• Binary Arithmetic - Addition
• EXAMPLE Using Triple Addition
• Binary Subtraction
• Binary Subtraction
• 2's Complement Subtraction
• Decimal Subtraction by Complementary Addition - Demonstration
• Binary Subtraction by Complementary Addition
• REPRESENTING NEGATIVE NUMBERS
• Remarks on two's complement
• WHY 2's-COMPLEMENT?

Binary Multiplication and Division

• Binary Multiplication
• Binary Multiplication by Repeated Addition
• Binary Multiplication by "Long Multiplication"
• Binary Multiply - Repeated Shift and Add
• Binary Division
• Binary Division by Repeated Subtraction
• Binary Division by Shift and Subtract

• Boolean Logic and Algebra
• Tables of Boolean Logic "Arithmetic" In Terms of "True and False"
• Tables of Boolean Logic "Arithmetic" In Terms of "0 and 1"
• Boolean Expressions
• Boolean Notations
• Graded Activities
  • EXAMPLES USING PROGRAMMING NOTATION - Exercise 1
  • EXAMPLES USING BOOLEAN NOTATION - Exercise 2
• Boolean Algebra
• Boolean Algebra Exercise

Truth Tables

• Problem Solving with Truth Tables
• Truth Functions Defined as Truth Tables
• Example: a simple Boolean function
• Using Truth Tables
• Proving the Equivalence of Boolean Equations - I
• Proving the Equivalence of Boolean Equations - II
• Proving the Equivalence of Boolean Equations - III

Truth Tables (cont'd)

• Discover Boolean Equations
• Truth Table to Boolean Expression
• 1-Column Addition - Three Digit Addition
• Boolean Expressions and Algorithms
• Boolean Expressions and Algorithms II

• Digital Circuits - A Quick History
• Mechanical Switching
• Mechanical Switching - Relays
• Transistors, Gates, and Circuits
• Gates
• Circuits
• From Boolean functions to circuit diagrams
• Tables to Expressions

Circuits

• Boolean Terms to Circuits
• Polish Notation
• Boolean Terms to Circuits
• Truth Table to Boolean Expression - Example(Exclusive OR)
• Circuit Design