Number Systems For Computer Scientists Course Syllabus

Overview: This course provides a focused introduction to the number systems that underpin computing, designed for beginners with no programming background. You'll build a solid mathematical foundation by learning how computers represent and manipulate numbers. Through clear explanations and interactive exercises, you'll master binary, octal, and hexadecimal systems, perform binary arithmetic, understand signed number representations, and explore fixed-point and floating-point formats. The course also covers essential data encoding concepts used in computer memory. With approximately 2 hours of total content, this hands-on course prepares aspiring computer scientists for deeper study in systems programming, embedded development, and low-level software engineering.

Module 1: Introduction to Number Systems

Estimated time: 0.2 hours

• Role of number systems in computing
• Overview of decimal, binary, octal, and hexadecimal systems
• Understanding positional (place-value) notation
• Course structure and learning objectives

Module 2: Decimal, Binary, Octal & Hexadecimal Conversions

Estimated time: 0.3 hours

• Place-value principles across number bases
• Converting decimal to binary using division-remainder method
• Converting decimal fractions to binary using multiplication-fraction method
• Conversion between binary, octal, and hexadecimal
• Reverse conversion from any base back to decimal

Module 3: Binary Arithmetic & Two’s-Complement

Estimated time: 0.4 hours

• Binary addition and subtraction rules
• Detection and implications of overflow in fixed-width binary
• Representation of negative numbers using two’s-complement
• Calculating two’s-complement for signed integers
• Interpreting two’s-complement binary values correctly

Module 4: Fixed-Point Notation

Estimated time: 0.25 hours

• Concept of scaling factors in fixed-point representation
• Allocating integer and fractional bits in binary
• Trade-offs between precision and range
• Performing fixed-point binary addition
• Encoding decimal fractions in fixed-point format

Module 5: IEEE-754 Floating-Point Representation

Estimated time: 0.5 hours

• Structure of IEEE-754 single-precision format
• Sign, exponent, and mantissa components
• Understanding exponent bias and normalized numbers
• Denormalized (subnormal) values and special cases
• Rounding modes and representation limits (NaN, infinity)

Module 6: Computer Storage & Encoding Basics

Estimated time: 0.2 hours

• Byte ordering: little-endian vs. big-endian
• Interpreting multi-byte values in memory
• ASCII character encoding fundamentals
• Introduction to Unicode and character representation
• Reading memory dumps for numeric and string data

Prerequisites

• Basic arithmetic skills (addition, subtraction, multiplication, division)
• No programming experience required
• Familiarity with grade-school math concepts

What You'll Be Able to Do After

• Differentiate between decimal, binary, octal, and hexadecimal number systems
• Convert numbers accurately between different bases
• Perform binary arithmetic and interpret two’s-complement signed values
• Encode and decode fixed-point binary representations of decimal fractions
• Explain IEEE-754 floating-point structure and interpret special values