Sign magnitude, one's complement, two's complement

Chuck Guzis cclist at
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> 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.


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