sign magnitude, ones complement, two's complement

[Mantorok Redgormor]

From least to greatest is it

sign magnitude
ones complement
two's complement

Where sign magnitude is the least way to represent integers
and two's complement is the best way to represent integers?

What are the pitfalls of them?

 

[Glen Herrmannsfeldt]

I doubt if sign magnitude has ever been used in a popular US computer. The
disadvantage of ones complement is that there are two representations for 0,
"positive" zero and negative zero. OTOH subtraction is less onerous with a
ones complement hardware design.

I believe the IBM 7090. But then they internally convert to ones complement
to do addition and subtraction.

Multiply and divide are easier in sign magnitude, and I believe divide is
done that way on most computers now.

Two's complement is certainly the dominant form in current computers.

Except for those made by Univac.

-- glen

 

[osmium]

sign magnitude
ones complement
two's complement

What are the pitfalls of them?

I doubt if sign magnitude has ever been used in a popular US computer. The
disadvantage of ones complement is that there are two representations for 0,
"positive" zero and negative zero. OTOH subtraction is less onerous with a
ones complement hardware design.

Two's complement is certainly the dominant form in current computers.

 

[Gordon Burditt]

From least to greatest is it

Least to greatest *WHAT*? Number of transistors in the CPU
to implement it? Tax rate? Weight of the documentation?

sign magnitude
ones complement
two's complement

Where sign magnitude is the least way to represent integers
and two's complement is the best way to represent integers?

Which is better, rat poison, a condom, or a Pepsi? It does rather
depend on what you want it for.

What are the pitfalls of them?

Unless you are designing a CPU or selecting one to buy, you don't
get to choose, and there are many MANY factors much more important
than this (like availability of a good compiler for it).

Gordon L. Burditt

 

[osmium]

I believe the IBM 7090. But then they internally convert to ones complement
to do addition and subtraction.

I'll be damned! And also the 7094 according to this link. Just to cloud
the issue they use twos complement for some index fiddling if you look at
the instruction repertoire; which is also on this site.

http://www.frobenius.com/binary.htm

 

[CBFalconer]

I doubt if sign magnitude has ever been used in a popular US
computer. The disadvantage of ones complement is that there are
two representations for 0, "positive" zero and negative zero.
OTOH subtraction is less onerous with a ones complement hardware
design.

Two's complement is certainly the dominant form in current
computers.

Actually arithmetic is more convenient in 2's complement, because
there is no need for end-around-carries.

However negation of a value is simpler in 1's complement. By
making the basic arithmetic operation a subtractor (rather than an
adder) you can avoid negative zero ever appearing, thus allowing
use of that value as a trap (e.g. uninitialized).

 

[Eric Sosman]

I doubt if sign magnitude has ever been used in a popular US computer.

The first computer I ever programmed used signed magnitude.
Was it "popular?" Hard to tell, but IBM thought enough of the
design to build the machines and offer them in a range of sizes
(twenty, forty, or sixty thousand decimal digits of memory).

 

[Joe Wright]

The first computer I ever programmed used signed magnitude.
Was it "popular?" Hard to tell, but IBM thought enough of the
design to build the machines and offer them in a range of sizes
(twenty, forty, or sixty thousand decimal digits of memory).

Upthread, someone mentioned the last might have been the IBM 7094 which
came out in Jan 1963 and was the last of the 'Old Iron' before the
'Modern' IBM 360 and later. How 'popular' could the 7094 have been? How
many of them were built? I don't know the number. 100? More?

My first computer was the Philco 2000/212 which came out the same month
as the 7094. In long suit we had 32K of 48-bit (8-character) words of
RAM in four 8K banks. Each bank had a cycle time of 1.1 microseconds.
Bank selection was done in the low order two bits of address so that we
could get four 48-bit words every 1.1 usecs. This was 'core' memory with
real magnetic cores.

We left the 7094 for dead.

Philco Computers, Willow Grove, PA, R.I.P.

 

[Glen Herrmannsfeldt]

(snip)


Actually arithmetic is more convenient in 2's complement, because
there is no need for end-around-carries.

With popular adder designs end-around carry isn't hard to do, and shouldn't
be slower. It complicates serial adders, but since the PDP-8S I don't know
that there have been any machines with serial binary adders.

However negation of a value is simpler in 1's complement. By
making the basic arithmetic operation a subtractor (rather than an
adder) you can avoid negative zero ever appearing, thus allowing
use of that value as a trap (e.g. uninitialized).

Yes, negation can be complicated with two's complement, as it can overflow.
On some machines this means processing a trap or exception for that case.

-- glen