Positional Number Systems Full Review: Base Conversions, Fractions, Signed Numbers, Addition

In this video, I give a full review of number systems for digital design, computer organization, and intro computer engineering courses. We start with the vocabulary and syntax of positional number systems (base, radix, digits, most and least significant bits) and build the summation representation that explains how every number system works. From there, we cover base conversions between decimal, binary, octal, and hexadecimal, then extend the same summation approach to representing fractional quantities in binary. Next, we walk through unsigned binary addition step by step, and finish with signed number representations: signed magnitude, one's complement, and two's complement. Every topic includes worked examples explained through the mathematical summation approach, so you understand why each method works, not just how to do it. Whether you're studying for a midterm or final exam or learning binary for the first time, this review covers everything you need on number systems. 0:00 Intro 0:31 Vocabulary, Syntax & Summation Representation 2:30 Base Conversions 5:46 Representing Fractional Quantities & Precision 8:31 Grouping 10:23 Unsigned Addition & Overflow 12:14 Signed Numbers: Signed Magnitude, One's Complement, Two's Complement 18:52 Conclusion Subscribe for tomorrow's video :)