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

!!

Requirements

I recommend you start with Design a Floating Point Unit 1 - Numbers , where I introduce the basics of floating point numbers.

Description

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 , eeers and anyone who is curious about how computers work.



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