Design a Floating Point Unit 2 - Multiplier
What you'll learn
- Full Multiplier Design in Logisim
- Intuition from Excel (VBA) Simulations
- Normal and Subnormal Multiplication
- Overflow , Underflow
- Special Values (NaN , Infinity , Zero)
- Nearest Even Rounding
- Following IEEE754
- Not just how it's done but WHY it's done !!!
- I recommend you start with Design a Floating Point Unit 1 - Numbers , where I introduce the basics of floating point numbers.
Welcome to the course on designing a floating point multiplier
This course covers all the basics you need to know in order to understand how to design and simulate a single precision 32 bit floating point binary multiplier. I work through the design using a tool I created in Microsoft Excel (VBA) which allows us to see visibly what is happening when we multiply two 32 bit single precision floating point binary numbers together. From this tool a really great visual and intuitive understanding is gained and this will allow us to then write down the mathematical algorithm that we need to use to implement the floating point multiplier in the digital simulation tool called Logisim.
I work through the entire design in Logisim and explain how each section works. You will have access to all the simulation files and the Excel VBA code that I used to model the multiplication process. The design follows the IEEE754 standard for single precision values and includes both normal and subnormal numbers , special cases + and - zero , + and - infinity NaN (Not a Number) correct subnormal rounding injection using nearest even value (as per IEEE754) , pre normalisation of subnormal numbers , extension of exponent range to 9 bits , overflow and underflow flags , not exact flag.
If like me you were stuck trying to find a practical (not a black box) course on a floating point unit (FPU) then this series of courses is for you.
Good Luck with the course.
Who this course is for:
- Computer scientists , engineers and anyone who is curious about how computers work.
I am a graduate in Communications Engineering from Edinburgh University. I have spent my adult life working in the communications industry. First as an integrated circuit designer then in mobile telecomms. My first love is mathematics and the application of mathematics to engineering problems. I also have a love of learning and teaching. Mathematics should be fun and enjoyable and an intuitive understanding should be gained first and foremost. Comprehension is king.