I'm trying to think of what one-third looks like when represented by two's
complement. What is its length? I'm not schur. It would be a DWORD in
assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
--
LS
24  1446 
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.com. ..
I'm trying to think of what one-third looks like when represented by two's
complement. What is its length? I'm not schur. It would be a DWORD in
assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
>
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.com. ..
>I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
--
LS
Lane Straatman wrote:
"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.com. ..
I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
Every possible bit pattern is a potential valid representation of the
best approximation to one-third, or even the exact representation of
it. There are practically no requirements on how a float is stored in
memory.
As Army1987 asked, what did you *really* mean?
"Lane Straatman" <in*****@invalid.netwrote in message
>
"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
>>
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.com ...
>>I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
Do you know what sign, mantissa and exponent mean, in relation to floating
point numbers?
--
Free games and programming goodies. http://www.personal.leeds.ac.uk/~bgy1mm
"Harald van D?k" <tr*****@gmail.comwrote in message
news:11**********************@l77g2000hsb.googlegr oups.com...
Lane Straatman wrote:
>"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
>
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.com. ..
I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what
one-third
looks like with two's complement representation and a length of 32
bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
Every possible bit pattern is a potential valid representation of the
best approximation to one-third, or even the exact representation of
it. There are practically no requirements on how a float is stored in
memory.
That's what I thought. How is it usually represented?
--
"Malcolm McLean" <re*******@btinternet.comwrote in message
news:FN******************************@bt.com...
>
"Lane Straatman" <in*****@invalid.netwrote in message
>>
"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
>>>
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.co m...
I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what
one-third looks like with [some reasonable representation] and a length
of 32 bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
Do you know what sign, mantissa and exponent mean, in relation to floating
point numbers?
There was a recent thread with Joe Wright and others that is probably as
much as I know about it. The sign will take a bit. The mantissa is the a
in the a**x. The exponent is the exponent, x.
--
On Mon, 26 Mar 2007 16:41:16 -0400, "Lane Straatman"
<in*****@invalid.netwrote:
>
"Harald van D?k" <tr*****@gmail.comwrote in message
news:11**********************@l77g2000hsb.googleg roups.com...
>Lane Straatman wrote:
>>"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.com ...
I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what
one-third
looks like with two's complement representation and a length of 32
bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
Every possible bit pattern is a potential valid representation of the
best approximation to one-third, or even the exact representation of
it. There are practically no requirements on how a float is stored in
memory.
That's what I thought. How is it usually represented?
At the risk of spoiling all the fun, I suggest you Google for "IEEE
floating point", which should get you lots of information.
--
Al Balmer
Sun City, AZ
Lane Straatman wrote:
"Harald van D?k" <tr*****@gmail.comwrote in message
>Every possible bit pattern is a potential valid representation of the
best approximation to one-third, or even the exact representation of
it. There are practically no requirements on how a float is stored in
memory.
That's what I thought. How is it usually represented?
#include <stdio.h>
#include <string.h>
#include <float.h>
int main(void)
{
float fltvalue = 1. / 3.;
double dblvalue = 1. / 3.;
long double lngdblvalue = 1.L / 3.;
unsigned char fltchars[sizeof fltvalue], dblchars[sizeof dblvalue],
lngdblchars[sizeof lngdblvalue];
size_t i;
printf("Every implementation is free to choose its own\n"
"method for storing floating point values.\n"
"Here is how one implementation stores 1/3.\n");
memcpy(fltchars, &fltvalue, sizeof fltvalue);
printf("As float 1/3 = %.*g\nHex: ", FLT_DIG, fltvalue);
for (i = 0; i < sizeof fltvalue; i++)
printf("%u ", fltchars[i]);
printf("\n\n");
memcpy(dblchars, &dblvalue, sizeof dblvalue);
printf("As double 1/3 = %.*g\nHex: ", DBL_DIG, dblvalue);
for (i = 0; i < sizeof dblvalue; i++)
printf("%u ", dblchars[i]);
printf("\n\n");
memcpy(lngdblchars, &lngdblvalue, sizeof lngdblvalue);
printf("As long double 1/3 = %.*Lg\nHex: ", LDBL_DIG, lngdblvalue);
for (i = 0; i < sizeof lngdblvalue; i++)
printf("%u ", lngdblchars[i]);
printf("\n\n");
return 0;
}
Every implementation is free to choose its own
method for storing floating point values.
Here is how one implementation stores 1/3.
As float 1/3 = 0.333333
Hex: 171 170 170 62
As double 1/3 = 0.333333333333333
Hex: 85 85 85 85 85 85 213 63
As long double 1/3 = 0.333333333333333333
Hex: 171 170 170 170 170 170 170 170 253 63 0 0
"Lane Straatman" <in*****@invalid.netwrote in message
news:5K******************************@comcast.com. ..
>
"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
>>
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.com ...
>>I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
00111110101010101010101010101011
--
Fred L. Kleinschmidt
Boeing Associate Technical Fellow
Aero Stability and Controls Computing
"Lane Straatman" <in*****@invalid.netwrote in message "Malcolm McLean"
<re*******@btinternet.comwrote in message
>Do you know what sign, mantissa and exponent mean, in relation to
floating point numbers?
There was a recent thread with Joe Wright and others that is probably as
much as I know about it. The sign will take a bit. The mantissa is the a
in the a**x. The exponent is the exponent, x.
Nearly right.
IEEE standard floating point number use something very similar to scientific
notation.
2000 is 2 * 10^3 in this notation.
By convention there is only one decimal digit before the point, so
2300 is 2.3 * 10^3
Numbers below one have negative exponents
0.023 = 2.3 * 10^-2 (mnemonic, count the zeroes, including the leading one)
2.3 itself is 2.3 * 10^0.
Floating point numbers are basically just the same, but in binary. Since the
leading most significant binary digit must always be one, most
representations including IEEE save a bit by omitting it. There is one
exception to this rule, zero, so zero is represented specially by all bits
zero. Since zero is 10^-inf, it makes sense to store exponents in a sign
magnitude encoding rather than twos complement, so that 0 is the lowest, 1
= -127 or whatever, and so on. The sign bit is self explanatory.
Finally there are a few special representations for infinity, not a number,
and what are called denormalised numbers, but you can ignore those for now.
By looking at the bit patterns in your compiler, you should be able to work
out how many bits are allocated to each section, and what the exponent
encoding is. Start with one and minus one to get the sign bit.
--
Free games and programming goodies. http://www.personal.leeds.ac.uk/~bgy1mm
"Lane Straatman" <in*****@invalid.netwrites:
I'm trying to think of what one-third looks like when represented by two's
complement. What is its length? I'm not schur. It would be a DWORD in
assembly. In c, it would be (I think:)
float r = (float)(one third)
float r = 1.0/3.0;
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
It looks like this:
00000000000000000000000000000000
Two's-complement is a representation for signed integers, which cannot
represent fractional values.
If you're asking what 1.0/3.0 looks like in a floating-point
representation, it depends on which representation is used. The IEEE
standard is most common; a web search should turn up documentation.
--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"
Keith Thompson <ks***@mib.orgwrites:
"Lane Straatman" <in*****@invalid.netwrites:
>I'm trying to think of what one-third looks like when represented by two's
complement. What is its length? I'm not schur. It would be a DWORD in
assembly. In c, it would be (I think:)
float r = (float)(one third)
float r = 1.0/3.0;
[snip]
I thought Lane Straatman's name looked familiar; I should have checked
before posting a followup.
Lane Straatman, in my opinion, is a troll; see
<http://groups.google.com/group/comp.lang.c/msg/a4cc7d2a141439a7>,
which references
<http://groups.google.com/group/comp.std.c/msg/d91bae8783a38bde>.
Until and unless he publicly apologizes for his previous boorish
behavior, he'll get no further help from me. Others, as always, will
do as they wish.
--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"
On Mar 27, 8:59 am, Martin Ambuhl <mamb...@earthlink.netwrote:
printf("As float 1/3 = %.*g\nHex: ", FLT_DIG, fltvalue);
for (i = 0; i < sizeof fltvalue; i++)
printf("%u ", fltchars[i]);
Here is how one implementation stores 1/3.
As float 1/3 = 0.333333
Hex: 171 170 170 62
That's an unconventional use of "Hex" :)
On Mar 27, 8:55 am, "Lane Straatman" <inva...@invalid.netwrote:
The sign will take a bit. The mantissa is the a in the a**x.
The exponent is the exponent, x.
In the implementation I have looked at, it is
a * 2**x
where 'a' is represented as a binary fraction between 0 and 1,
for example 0.75 would be 110000...0
Note that you would never need 'a' being less than 0.5, because
you could then scale it by doubling 'a' and subtracting one from 'x'.
So you can actually drop the first bit of 'a', assuming it always
to be 1, and use that storage for the sign bit.
"Keith Thompson" <ks***@mib.orgwrote in message
news:ln************@nuthaus.mib.org...
Keith Thompson <ks***@mib.orgwrites:
>"Lane Straatman" <in*****@invalid.netwrites:
>>I'm trying to think of what one-third looks like when represented by
two's
complement. What is its length? I'm not schur. It would be a DWORD in
assembly. In c, it would be (I think:)
float r = (float)(one third)
float r = 1.0/3.0;
[snip]
I thought Lane Straatman's name looked familiar; I should have checked
before posting a followup.
Lane Straatman, in my opinion, is a troll; see
<http://groups.google.com/group/comp.lang.c/msg/a4cc7d2a141439a7>,
which references
<http://groups.google.com/group/comp.std.c/msg/d91bae8783a38bde>.
Until and unless he publicly apologizes for his previous boorish
behavior, he'll get no further help from me. Others, as always, will
do as they wish.
Your "help" has consisted of shitting on my threads; your abscence is
welcome. I liked you a lot more as the Other Keith.
--
Old Wolf wrote:
On Mar 27, 8:59 am, Martin Ambuhl <mamb...@earthlink.netwrote:
> printf("As float 1/3 = %.*g\nHex: ", FLT_DIG, fltvalue);
for (i = 0; i < sizeof fltvalue; i++)
printf("%u ", fltchars[i]);
Here is how one implementation stores 1/3.
As float 1/3 = 0.333333
Hex: 171 170 170 62
That's an unconventional use of "Hex" :)
Yes, I erred. Thanks for noticing.
To the OP: my "%u " should be "%x ".
"Fred Kleinschmidt" <fr******************@boeing.comwrote in message
news:JF********@news.boeing.com...
>
"Lane Straatman" <in*****@invalid.netwrote in message
news:5K******************************@comcast.com. ..
>>
"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
>>>
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.co m...
I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what
one-third looks like with two's complement representation and a length
of 32 bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
00111110101010101010101010101011
I'm actually going to try to code this tonight, but there's no guarantees
because I've got a poker game to go to. I think that Fred's answer is going
to be what my C IDE on windows has. I would be surprised to find popular
implementations that don't waffle between zero and one on this for the
bigger part of it.
It's been a while since I put a semicolon on the end of an executable
statement.
--
LS
>"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
>news:es******************************@comcast.com ...
>>I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
>"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
>Two's complement is a representation for signed integers.
What did you *really* mean?
Indeed.
In article <5K******************************@comcast.com>
Lane Straatman <in*****@invalid.netwrote:
>I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
The format of floating-point numbers is specified quite loosely.
For some details on some actual representations (particularly the
now-common IEEE format), see <http://web.torek.net/torek/c/numbers.html>.
--
In-Real-Life: Chris Torek, Wind River Systems
Salt Lake City, UT, USA (40°39.22'N, 111°50.29'W) +1 801 277 2603
email: forget about it http://web.torek.net/torek/index.html
Reading email is like searching for food in the garbage, thanks to spammers.
Lane Straatman wrote:
"Keith Thompson" <ks***@mib.orgwrote in message
.... snip ...
>>
I thought Lane Straatman's name looked familiar; I should have
checked before posting a followup.
Lane Straatman, in my opinion, is a troll; see
<http://groups.google.com/group/comp.lang.c/msg/a4cc7d2a141439a7>,
which references
<http://groups.google.com/group/comp.std.c/msg/d91bae8783a38bde>.
Until and unless he publicly apologizes for his previous boorish
behavior, he'll get no further help from me. Others, as always,
will do as they wish.
Your "help" has consisted of shitting on my threads; your abscence
is welcome. I liked you a lot more as the Other Keith.
Looks like Keith was right - PLONK.
--
Chuck F (cbfalconer at maineline dot net)
Available for consulting/temporary embedded and systems.
<http://cbfalconer.home.att.net>
--
Posted via a free Usenet account from http://www.teranews.com
"CBFalconer" <cb********@yahoo.comwrote in message
news:46***************@yahoo.com...
Lane Straatman wrote:
>"Keith Thompson" <ks***@mib.orgwrote in message
... snip ...
>>>
I thought Lane Straatman's name looked familiar; I should have
checked before posting a followup.
Lane Straatman, in my opinion, is a troll; see
<http://groups.google.com/group/comp.lang.c/msg/a4cc7d2a141439a7>,
which references
<http://groups.google.com/group/comp.std.c/msg/d91bae8783a38bde>.
Until and unless he publicly apologizes for his previous boorish
behavior, he'll get no further help from me. Others, as always,
will do as they wish.
Your "help" has consisted of shitting on my threads; your abscence
is welcome. I liked you a lot more as the Other Keith.
Looks like Keith was right - PLONK.
I won't mind your absence either, OS bigot.
--
Lane Straatman wrote:
>
I'm trying to think of what one-third looks like when represented by two's
complement. What is its length? I'm not schur. It would be a DWORD in
assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
I think the question can be stated unambiguously if I ask what one-third
looks like with two's complement representation and a length of 32 bits.
/*
** two's complement representation is for negative integers.
*/
/* BEGIN output from bitstr.c */
0.333333 = 00111110101010101010101010101011
/* END output from bitstr.c */
/* BEGIN bitstr.c */
#include <limits.h>
#include <stdio.h>
#define STRING "%15f = %s\n"
#define E_TYPE float
#define INITIAL ((float)(1.0 / 3))
#define FINAL INITIAL
#define INC(E) ((E) *= 2)
typedef E_TYPE e_type;
void bitstr(char *str, const void *obj, size_t n);
int main(void)
{
e_type e;
char ebits[CHAR_BIT * sizeof e + 1];
puts("\n/* BEGIN output from bitstr.c */\n");
e = INITIAL;
bitstr(ebits, &e, sizeof e);
printf(STRING, e, ebits);
while (FINAL e) {
INC(e);
bitstr(ebits, &e, sizeof e);
printf(STRING, e, ebits);
}
puts("\n/* END output from bitstr.c */");
return 0;
}
void bitstr(char *str, const void *obj, size_t n)
{
unsigned mask;
const unsigned char *byte = obj;
while (n-- != 0) {
mask = ((unsigned char)-1 >1) + 1;
do {
*str++ = (char)(mask & byte[n] ? '1' : '0');
mask >>= 1;
} while (mask != 0);
}
*str = '\0';
}
/* END bitstr.c */
--
pete
Lane Straatman wrote:
"Harald van D?k" <tr*****@gmail.comwrote in message
news:11**********************@l77g2000hsb.googlegr oups.com...
>Lane Straatman wrote:
>>"Army1987" <pl********@for.itwrote in message
news:eu**********@tdi.cu.mi.it...
"Lane Straatman" <in*****@invalid.netha scritto nel messaggio
news:es******************************@comcast.c om...
I'm trying to think of what one-third looks like when represented by
two's complement. What is its length? I'm not schur. It would be a
DWORD in assembly. In c, it would be (I think:)
float r = (float)(one third)
My syntax is somewhat wanting.
>
I think the question can be stated unambiguously if I ask what
one-third
looks like with two's complement representation and a length of 32
bits.
Two's complement is a representation for signed integers.
What did you *really* mean?
I knew I was in trouble there. What possiblities does one have for
representing one-third as a float in C, in particular with 32 bits?
Every possible bit pattern is a potential valid representation of the
best approximation to one-third, or even the exact representation of
it. There are practically no requirements on how a float is stored in
memory.
That's what I thought. How is it usually represented?
00111110 10101010 10101010 10101011
Exp = 125 (-1)
11111111
Man = .10101010 10101010 10101011
3.33333343e-01
0.333333
...is one possibility.
--
Joe Wright
"Everything should be made as simple as possible, but not simpler."
--- Albert Einstein ---
"pete" <pf*****@mindspring.comwrote in message
news:46***********@mindspring.com...
Lane Straatman wrote:
>[what's one third look like]
/* BEGIN bitstr.c */
#include <limits.h>
#include <stdio.h>
#define STRING "%15f = %s\n"
#define E_TYPE float
#define INITIAL ((float)(1.0 / 3))
#define FINAL INITIAL
#define INC(E) ((E) *= 2)
typedef E_TYPE e_type;
void bitstr(char *str, const void *obj, size_t n);
int main(void)
{
e_type e;
char ebits[CHAR_BIT * sizeof e + 1];
puts("\n/* BEGIN output from bitstr.c */\n");
e = INITIAL;
bitstr(ebits, &e, sizeof e);
printf(STRING, e, ebits);
while (FINAL e) {
INC(e);
bitstr(ebits, &e, sizeof e);
printf(STRING, e, ebits);
}
puts("\n/* END output from bitstr.c */");
return 0;
}
void bitstr(char *str, const void *obj, size_t n)
{
unsigned mask;
const unsigned char *byte = obj;
while (n-- != 0) {
mask = ((unsigned char)-1 >1) + 1;
do {
*str++ = (char)(mask & byte[n] ? '1' : '0');
mask >>= 1;
} while (mask != 0);
}
*str = '\0';
}
/* END bitstr.c */
/* BEGIN output from bitstr.c */
0.333333 = 00111110101010101010101010101011
/* END output from bitstr.c */
Clean as a whistle.
--
LS
On Mon, 26 Mar 2007 22:21:28 +0100, "Malcolm McLean"
<re*******@btinternet.comwrote:
<snip>
Floating point numbers are basically just the same, but in binary. Since the
By convention, at present. C doesn't require binary for floating point
(it does for integers) and there are some fairly serious attempts
among the numerics people to move to decimal floating point.
leading most significant binary digit must always be one, most
representations including IEEE save a bit by omitting it. There is one
exception to this rule, zero, so zero is represented specially by all bits
Yes, and zero is all-bits-zero except optionally sign.
zero. Since zero is 10^-inf, it makes sense to store exponents in a sign
magnitude encoding rather than twos complement, so that 0 is the lowest, 1
= -127 or whatever, and so on. The sign bit is self explanatory.
The IEEE representation of the exponent is biased, not S&M.
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