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Last modified: 17 February 2007 13:08:34.


Math
Ok so I guess I have become member of the NERD club...


Let's count like this...

1, 2, 4, 8, 16, 32, 64, 128, 256, 512 .... extend all these numbers by small areas of other numbers in the range  -2, -1, 0, 1, 2... we then get

-1,0,1,2,3,4,5,6,7,8,9,10,14,15,16,17,18,30,31,32,33,34,62, 63,64,65,66,126,127,128,129,130,254,255,256,257,258,510,511, 512,513,514,1022,1023,1024,1025,1026,2046,2047,2048,2049, 2050,4094,4095,4096,4097,4098,8190,8191,8192,8193,8194, ...

click below...

ULTRA NURD 1

Another way of formulating this could be as islands of linear number sequences in the binary number space - huh?

or how about these numbers?

-1,0,1,7,8,9,15,16,17,127,128,129,255,256,257,2047,2048,2049,4095,4096,4097, ...


ULTRA NURD 2


 Observe the numbers 8, 16 and 128, 256 and 2048, 4096... these numbers form the base series.

So what's the point in all this? Well most HW and SW are based on binary (2^n) organized "components", so my thinking behind this would be that errors in the design or implementation of either HW or SW would be either when you take another extra bit into account or when you extend a design from lets say 8 to 16 bits, 16 to 32 bits or something like that. In these cases you may have some 8 bit Accumelator perfectly in shape to handle eg. "12 + 46" but what happens at the limits ? when you add 128 and 128 or 127 and 129 ?.... - those are the ideas behind my thinking.

Suppose a CPU design og SW design is 90% debugging and then finally when it all works well 10% verification test - suppose my tiny subset of integers could provide a quick way to point to some design error in the design / coding phase - then potentially errors could be found earlier - or suppose you want to run tests over a huge address space, huge temperature range, huge clock setting range etc. - now if you should do that with all the possible numbers that would take some time X ..... with a limited subset of numbers it would take a fraction of X

I just love thinking about such matters...        

And so some time later ... I came up with a new series of numbers ... even smaller than the  previous...

0,1,2,3,4,7,8,15,16,127,128,255,256,32767,32768,65535,65536,4294967295,4294967296,2147483647,2147483648,...

Notice the base numbers as 1,2,4,16,256,...

ULTRA NURD 3   


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