Sign magnitude, one's complement, two's complement
Chuck Guzis
cclist at sydex.com
Sat Aug 22 20:15:38 CDT 2015
On 08/22/2015 04:40 PM, Paul Koning wrote:
>
>> On Aug 22, 2015, at 6:27 PM, Chuck Guzis <cclist at sydex.com> wrote:
>>
>> ...FLoating point can engender some interesting representations.
>> Consider the exponent field on the aforementioned CDC 6000 series.
>> It's a "biased by 2000 octal) system--and the assumed binary point
>> of the mantissa is to the right of the LSB. So, 2000 0000 0000
>> 0000 0001 octal = 1 exactly.
>
> EL-X8 doesn't use the bias, so the floating point representation of
> an integer under 2^39 is the same as the integer representation. And
> the rule for normalizing float values preserves that (normalization
> makes the exponent as close to zero as possible -- rather different
> than the usual rule).
I recall the "integer multiply" feature (i.e. optional) available on the
6000. IXi Xj*Xk, but it didn't provide any more precision than the
usual unnormalized double-precision multiply DXi Xj*Xk, but saved some
time spent fiddling with exponent fields. There was no corresponding
Integer divide. So the integer adds would give the usual 60 bits of
precision, while the integer multiply gave 48.
On the other hand, the unnormalized integer mantissas could be very
useful. One such is an integer divide by a constant. Good enough for
small magnitude numbers.
All of that went out the window on the STAR, however. A more
traditional normalized two's complement format was used.
--Chuck
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