"Decimals" word in binary space

[Morten Leikvoll]

Im looking for an equivalent word for "decimal" in a binary number. The
"deci" says it's all about base 10 numbers, but I miss an official term for
the 1/(2^n) digits. I'm using "binimals" in lack of a better word.
Also, is there a binary world equivalent for the "decimal" point?

 

[Morten Leikvoll]

I don't believe "decimals" is correctly used to refer to decimal digits.
Maybe Decimal places... Binary digits (or binary bits or just bits) and
binary point are the accepted terms you seek.

The examples shown in http://www.merriam-webster.com/dictionary/decimals
says

"The number 67.398 is a decimal. It is equal to the whole number 67 plus the
decimal.398.
Seven-tenths written as a decimal is.7. Seven-tenths written as a fraction
is {frac7.
The decimal.2 is equal to the fraction {frac2."

(never seen the {frac notation before though)
There is the integer, or leading digits part. I guess the rest is called
non-integer part, but it sounds a bit clumsy. Is there another word? In my
native language the word most similar to decimal is used for the non integer
part only. And if you look in the cell formatting of a spread sheet, the
term "decimal places" refer to the # of digits to the right of the dot.
I guess I could call those digits the modulo1 part of the value as well.
Those terms works with any number base, but also clumsy.

I would like an easy way to express a reference to the N'th digit of either
the integer or the modulo1 part and I'm not really happy with my current
options..

 

On Wednesday, August 15, 2012 6:35:55 AM UTC-5, Morten Leikvoll wrote:

Im looking for an equivalent word for "decimal" in a binary number. The "deci" says it's all about base 10 numbers, but I miss an official term for the 1/(2^n) digits. I'm using "binimals" in lack of a better word. Also, is there a binary world equivalent for the "decimal" point?

I don't believe "decimals" is correctly used to refer to decimal digits. Maybe Decimal places... Binary digits (or binary bits or just bits) and binary point are the accepted terms you seek.

Andy

 

[Andy Bartlett]

"Morten Leikvoll" <mleikvol@yahoo.nospam> wrote in message
news:ssWdnbZrfZ4GFLbNnZ2dnUVZ8vKdnZ2d@lyse.net...

Im looking for an equivalent word for "decimal" in a binary number. The
"deci" says it's all about base 10 numbers, but I miss an official term
for the 1/(2^n) digits. I'm using "binimals" in lack of a better word.
Also, is there a binary world equivalent for the "decimal" point?

Do you mean hexadecimal where 4bit nibbles are used to describe each decade?

 

[Jon Elson]

Morten Leikvoll wrote:

Im looking for an equivalent word for "decimal" in a binary number. The
"deci" says it's all about base 10 numbers, but I miss an official term
for
the 1/(2^n) digits. I'm using "binimals" in lack of a better word.
Also, is there a binary world equivalent for the "decimal" point?
The correct term, I think, is decimal fraction, so the equivalent

would be binary fraction.

Jon

 

[glen herrmannsfeldt]

Morten Leikvoll <mleikvol@yahoo.nospam> wrote:

Im looking for an equivalent word for "decimal" in a binary number.
The "deci" says it's all about base 10 numbers, but I miss an
official term for the 1/(2^n) digits. I'm using "binimals"
in lack of a better word.

It seems that decimal is used for both the base and for numbers,
especially fractional numbers, written in it. Also for binary.

Exactly why, I don't know.

More specifically, it seems that people sometimes use the word
"decimal" as short for "decimal fraction" or digits after the
decimal point.

Also, is there a binary world equivalent for the "decimal" point?

There is a binary point, also octal point and hexadecimal point
if you happen to be in one of those radices, and generic radix
point.

Metric fractions are decimal for obvious reasons, but why are
fractions of an inch usually binary? (Though written as fractions
with powers of two in the denominator.)

-- glen

 

[glen herrmannsfeldt]

Jon Elson <jmelson@wustl.edu> wrote:

(snip)

The correct term, I think, is decimal fraction, so the equivalent
would be binary fraction.

Yes, often shortened to decimal.

Reminds me, that I never understood how "application program" got
reduced to "application" and then "app." Doesn't sound right to me.

-- glen

 

[Brian Davis]

Morten Leikvoll wrote:

There is the integer, or leading digits part. I guess the rest is called
non-integer part, but it sounds a bit clumsy. Is there another word?
snip

I would like an easy way to express a reference to the N'th digit of either
the integer or the modulo1 part and I'm not really happy with my current
options..

The notation I'm familiar with refers to the various portions of a
two's complement signed fractional binary number as follows [Ref 1]:

siii.ffff
s : sign bit
i : integer bit
.. : binary point
f : fractional bit

The individual bits are then referred to by their binary weighting,
2^N, where N can be negative for fractional formats.

For the above fraction
2^2 = most significant integer bit
2^0 = least significant integer bit
2^-1 = most significant fractional bit

The VHDL fixed point package [Ref 3] indexes fractional numbers
by using N directly in index and range expressions.

- Brian

References:

[Ref 1] "Fractional and Integer Arithmetic using the DSP56000 Family
of General-Purpose Digital Signal Processors", APR3/D Rev. 1
http://cache.freescale.com/files/dsp/doc/app_note/APR3.pdf

[Ref 2] "Fixed-Point Arithmetic: An Introduction", Randy Yates
http://personal.atl.bellsouth.net/y/a/yatesc/fp.pdf

[Ref 3] "Fixed Point Package User’s Guide", David Bishop
http://www.vhdl.org/fphdl/Fixed_ug.pdf

 

[Morten Leikvoll]

The notation I'm familiar with refers to the various portions of a
two's complement signed fractional binary number as follows [Ref 1]:
siii.ffff
s : sign bit
i : integer bit
. : binary point
f : fractional bit

Fair enough, but initially why cant we just adopt the minus sign for
negative numbers when writing. Ok, the machine implementation of it needs
the sign bit, but brain-mapping arithmetics with base10 to base2 (or any
base) becomes more complicated if you do it before implementation imho.

The individual bits are then referred to by their binary weighting,
2^N, where N can be negative for fractional formats.
For the above fraction
2^2 = most significant integer bit
2^0 = least significant integer bit
2^-1 = most significant fractional bit

so to keep the base10 terms, the 2^0'th bit would be the first integer
bit/digit, 2^1 would be the second and so on..
For the fraction, 2^(-1) would be the first fractional bit/digit, 2^(-2) the
second and so on.
Now, I do miss a compact word for "integer bit" and "fractional bit".

indexes fractional numbers
by using N directly in index and range expressions.

I had to give up using fractional types cause I was not satisfied with the
packages. I ended up using logic vectors and keeping track on the fractional
part myself. At least then I could blame myself if something went wrong..

 

[Morten Leikvoll]

This link also suggests that sometimes "decimals" are used for the
fractional part only : http://www.thefreedictionary.com/decimal
I would claim the word is a bit washed out if the definition is not clear.

 

[Tim Wescott]

On Wed, 15 Aug 2012 13:35:55 +0200, Morten Leikvoll wrote:

Im looking for an equivalent word for "decimal" in a binary number. The
"deci" says it's all about base 10 numbers, but I miss an official term
for the 1/(2^n) digits. I'm using "binimals" in lack of a better word.
Also, is there a binary world equivalent for the "decimal" point?

"Floating point" for the number, "radix" for the little dot.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

 

[Morten Leikvoll]

Im looking for an equivalent word for "decimal" in a binary number. The
"deci" says it's all about base 10 numbers, but I miss an official term
for the 1/(2^n) digits. I'm using "binimals" in lack of a better word.
Also, is there a binary world equivalent for the "decimal" point?

"Floating point" for the number, "radix" for the little dot.

Floating point number is the term used for numbers with a movable point. In
practice the numbers have a bitfield telling where the dot is in the cluster
of bits. It only suggests that the dot is just a "point". Nothing about the
numer base. But since the dot is base neutral, I guess its fine to use both
"dot" and "point".

According to mw.com, radix is Latin for "root". Meanings:
1: the base of a number system or of logarithms
2: the primary source

Your suggestions doesnt make any sense to me.

 

[Tim Wescott]

On Mon, 20 Aug 2012 11:43:53 +0200, Morten Leikvoll wrote:

Im looking for an equivalent word for "decimal" in a binary number.
The "deci" says it's all about base 10 numbers, but I miss an official
term for the 1/(2^n) digits. I'm using "binimals" in lack of a better
word. Also, is there a binary world equivalent for the "decimal"
point?

"Floating point" for the number, "radix" for the little dot.

Floating point number is the term used for numbers with a movable point.
In practice the numbers have a bitfield telling where the dot is in the
cluster of bits. It only suggests that the dot is just a "point".
Nothing about the numer base. But since the dot is base neutral, I
guess its fine to use both "dot" and "point".

According to mw.com, radix is Latin for "root". Meanings: 1: the base of
a number system or of logarithms 2: the primary source

Your suggestions doesn't make any sense to me.

That's because I was talking about usage in the English language, which
makes no sense. If you want to ask questions about a language and get
answers that make sense when you chase the words down to their roots, may
I suggest Esperanto, Klingon, or some other synthetic language?

I was using "little dot" instead of "point" to avoid any Language Nazis
who might feel inclined to try to drown me in erudition. Whatever it may
be technically, visually it's a little dot (well, a comma in Europe).

Re-reading your original post in light of what you're saying here, I
think you're talking of the decimals to the right of the radix point (and
yes, "radix point", or "radix" for short, is the term that's used, so by
practical linguistics it does -- ipso facto -- make sense). If so, then
I believe the usage among practitioners is "fractional part" (as opposed
to the "integer part", which is to the left of the radix point).

If you're interested in learning what practitioners use so that you can
write documents or questions that make sense to the masses try asking on
comp.dsp -- that's where I'd ask, and I'd be sure to get good answers.

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

 

[glen herrmannsfeldt]

Tim Wescott <tim@seemywebsite.com> wrote:

(snip, someone wrote)

Your suggestions doesn't make any sense to me.

That's because I was talking about usage in the English language, which
makes no sense. If you want to ask questions about a language and get
answers that make sense when you chase the words down to their roots, may
I suggest Esperanto, Klingon, or some other synthetic language?

I was using "little dot" instead of "point" to avoid any Language Nazis
who might feel inclined to try to drown me in erudition. Whatever it may
be technically, visually it's a little dot (well, a comma in Europe).

OK, but it seems to me that the OPs question related to the difference
between that ary suffix in binary, and the al suffix in decimal, octal,
or hexadecimal. That, in addition to the confusing use of the word
decimal to indicate a base 10 fraction.

But all that is completely separate from fixed vs. floating point.
You can do either in decimal, binary, or any other radix. The Fortran
standard allows for any radix greater than one, for either fixed
or floating point.

Re-reading your original post in light of what you're saying here, I
think you're talking of the decimals to the right of the radix point (and
yes, "radix point", or "radix" for short, is the term that's used, so by
practical linguistics it does -- ipso facto -- make sense). If so, then
I believe the usage among practitioners is "fractional part" (as opposed
to the "integer part", which is to the left of the radix point).

I disagree with shortening "radix point" to "radix", but otherwise
agree.

If you're interested in learning what practitioners use so that you can
write documents or questions that make sense to the masses try asking on
comp.dsp -- that's where I'd ask, and I'd be sure to get good answers.

-- glen

 

Two's Complement format and signed integer format are two different formats..

The MSB of two's complement format is NOT a "sign" bit. Sure, in two's complement, the MSB can be used to tell if the quantity is negative, but the other ("integer") bits are also interpretted differently based on the MSB. They do not represent the absolute value of the quantity.

Signed integer format uses a "sign bit" that ONLY indicates whether the quantity is negative or positive. The "integer" part of signed integer is the absolute value of the quantity.

Andy