Number Representations in Computer Hardware, Explained

[ma3mool]

Welcome to a fundamental area of computer design: how numbers are represented in hardware! This can ultimately mean the difference between a blazing fast machine and a costly $475 million bug – Pentium 4, anyone?

Read the full article here.

Number Representations in Computer Hardware, Explained

 

[m3tavision]

Thank you for this wonderful article...

We use to play number games in College... and leave binary messages on door boards..!

 

[madboyv1]

This was a great primer and a good read.

 

[kira setsu]

I'm not good enough at math to understand much but it was a very interesting read.

 

[Bamda]

This is an awesome article. Thanks for giving us a refresher on the magic of numbers in Computer Hardware.

 

[Hodor]

Excellent article.

 

[AdamNovagen]

This is the kind of article that got me on TS in the first place. Shame they turned out to only make up like 1 out of every 40 or 50, but I'm nevertheless grateful for this quality content.

 

[Tetr1s]

I had to read through this article twice to make sure I was retaining the information correctly lmao

 

[bl4C3y3]

Great article, thx a lot !

 

[John Staerck]

A very interesting article. Although for me it didn't really explain the need for the bias in the exponent field of floating point representations.

 

[ma3mool]

A very interesting article. Although for me it didn't really explain the need for the bias in the exponent field of floating point representations.

Excellent question. The short answer is that the bias allows you to get both positive and negative exponent values. So, if you want to get 2^-3, the bias allows you to encode it in a very straightforward way, by using the 8-bits for 124.

The longer answer is that it has to do with 2's complements, which isn't discussed here at all. It turns out that using a bias just makes life easier for the hardware, then having to interpret a 2's complement number and figure out if it is positive or negative.

 

[Random Commenter]

Good read, thanks.

One thing: it's a fundamental tenet, not tenant

 

[leanne martin]

Good read, thanks.

One thing: it's a fundamental tenet, not tenant

That's right 'coz 'a fundamental tenant' is one whose dogma pisses all over your karma...

 

[VcoreLeone]

This is the kind of article that got me on TS in the first place. Shame they turned out to only make up like 1 out of every 40 or 50, but I'm nevertheless grateful for this quality content.

F**k me if I or most of us will really, truly understand the math that cpu is doing. I think the majority comes here for tech news and review discussion.

 

[Rafael Colorado]

Excellent summary tells the story and the evolution up to AI number representation. Thanks.

 

[Antias]

Wow
I'm kinda shocked that I actually understood most (not all) of that...
Maybe there's life left in this 59 year old brain after all!
LOL
Thank you for an excellent post, I was quite engrossed to the point my coffee got cold, still held in my hand!

 

[elaynetrakand]

I don't have enough skill in math to grasp much, but it was a highly captivating read.

 

[madboyv1]

I enjoyed the re-read. *checks to see if I ever commented* Okay I'll take another one now.

 

[TheBigFatClown]

But wait?? My head hurts now. I thought AI was going to do all the math, and programming, and logic, and graphics so I could sit on my FAT XXX all day and do nothing? Isn't that what Jenson Huang said or whatever the hell his name is?

 

[hk2000]

Okay.....It is interesting, fascinating, enlightening and all the good adjectives.... but really, who the hell cares??? You don't even need to understand all of this to design a chip that does it for you. Even the most powerful computer does nothing more than the same basic operations: Add, subtract, divide, multiply and compare!

 

[mogo2k]

Enjoyed reading this article!
Thank you

 

[Belty]

Great wander down memory lane. and where we are evolving to. Thank you.
For a few of we more mature coders/engineers it would be nice to mention octal base representation.

I had to write some floating point code in Z80 assembler many moons ago which was a great introduction to number representation. It was amazing how many floating point calcs a 4 MHz 8 bit Z80 could execute in a second.