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Tanks and crushed corpses in Tiananmen Square? Journalists jailed for life for editorializing against Beijing? Professors forced from their universities for mentioning — in a classroom full of eager government informants — the Chinese-backed genocide in Darfur?

BGX13P22GA-V21R_Datasheet PDF

Tanks and crushed corpses in Tiananmen Square? Journalists jailed for life for editorializing against Beijing? Professors forced from their universities for mentioning — in a classroom full of eager government informants — the Chinese-backed genocide in Darfur?

It's funny how some things stick in your mind, isn't it? A few days ago I posted a blog on n-ary” (non-Boolean) Gray codes, and this rascally rapscallion of a topic has been bouncing back and forth like a Super Ball in my brain ever since.

Here's where I'm at so far. Let's start with the binary number system because that's the way I tend to think by default. In the case of binary, we can say that a Gray code is one in which only a single bit (binary digit) changes when transitioning from one state to another. A quick-and-easy technique for generating binary Gray codes that's easy to remember and use is as follows:

BGX13P22GA-V21R_Datasheet PDF

An example of this mirroring process (which is more correctly referred to as a reflected binary code”) used to generate a 3-bit gray code is as follows:

In particular, observe that performing one more step from 100 back to 000 also involves only a single bit transitioning.

BGX13P22GA-V21R_Datasheet PDF

Another technique is to commence with a state of all zeros, and to then generate a Gray code by always changing the least significant bit that results in a new state. Alternatively, we can just throw one together” by hand as follows:

BGX13P22GA-V21R_Datasheet PDF

So, why am I waffling on about this here? Well, until a reader posted a question in the blog referenced earlier, I hadn't really thought about n-ary Gray codes” (these are also known as a non-Boolean Gray codes” because they use non-Boolean values in their encodings).

Purely for the sake of discussion, let's start by playing with a 4-ary” or quaternary (base-4) number system, in which each digit may carry one of four values: 0, 1, 2 and 3. Now consider a standard quaternary count versus a Gray code quaternary equivalent (for the sake of simplicity we will experiment with 2-digit values):

Foundry customers: Just what the doctor ordered: Another foundry choice. The problem: With another competitor looming on the horizon, foundry vendors may have to cut their prices to keep customers aboard. So foundry customers will benefit.

Losers:

AMD: The fact that AMD broke the company into two parts and shed its fabs means one thing: It failed as an IDM. Wonder what Jerry Sanders, AMD's former boss, is thinking right now? I'm sure he's eating his words that ''real men have fabs.''

PC OEMS: The world has benefitted from two strong x86-based processor makers. It presents choices for customers and brings computing to a new level. For example, Intel and AMD pushed each other in the market, enabling new-fangled multicore designs.Now, AMD is betting the farm on Shanghai, its new 45-nm processor line. If that fails, will AMD ask for another bailout? And if AMD fails, will the market benefit?

IBM's fab club”: IBM's technology alliance develops processes and spreads the costs and risks among its members. It has been helpful to the foundry members of this club: Chartered and Samsung. The alliance has basically saved Chartered. Samsung gained logic technology that it struggled to develop on its own.China's SMIC also benefitted, although it's not an official ''fab club” member. SMIC licensed IBM's 45-nm process technology.

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