"Decimals" word in binary space

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. Ma= ybe Decimal places... Binary digits (or binary bits or just bits) and binar= y point are the accepted terms you seek.

Andy

The examples shown in

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..

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

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.

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

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

Jon

(snip)

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

er

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 =3D most significant integer bit 2^0 =3D least significant integer bit 2^-1 =3D 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 [Ref 2] "Fixed-Point Arithmetic: An Introduction", Randy Yates [Ref 3] "Fixed Point Package User=92s Guide", David Bishop

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.

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".

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..

This link also suggests that sometimes "decimals" are used for the fractional part only :

I would claim the word is a bit washed out if the definition is not clear.

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

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

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.

Two's Complement format and signed integer format are two different formats= .=20

The MSB of two's complement format is NOT a "sign" bit. Sure, in two's comp= lement, the MSB can be used to tell if the quantity is negative, but the ot= her ("integer") bits are also interpretted differently based on the MSB. Th= ey do not represent the absolute value of the quantity.=20

Signed integer format uses a "sign bit" that ONLY indicates whether the qua= ntity is negative or positive. The "integer" part of signed integer is the = absolute value of the quantity.=20

Andy