Why decibels and not scientific notation?

[IconicPCB]

No per unit is a linear quantity designed to make life simpler much as the logarithmic Bell and deciBell are.
As I said .. an engineer thing.

[electrolust]

And you can write "dB" without klugey substitutes for superscripts in plain text.  "^2" is ugly, although required in the format used in these posts.

Oh ^really?

[RogerRowland]

Oh ^really?

+¹ 

[DimitriP]

If I have a transmitter with an output power of 3x10^2 transmitting into a antenna with a gain of 23 over a path loss of 6.4x10-8 into a receiving antenna with a gain of 4.6 and the receiver needs an SNR of 18 in a 230kHz bandwidth to be able to demodulate the signal, what noise figure does it need?

Alternatively, if it's transmitting at +53dBm, through an antenna with a gain of 14dBi, over a path loss of 145dB into a receive antenna of . ...

Which would you rather work out?

Why do you need to work it out? Haven't you heard  of forums ?  ( I can resist all, but tempation )

[TimFox]

When you need to convert a ratio of monetary values to dB, remember to use the factor x10, not x20, since money is power.

[Simon]

decibels were devised for audible sound and out ears are logaritmic in response, so we hear a 30dB sound as three times as load as 10dB but the sound power is 100x stronger.

the scale was found to be very convinient for electronics as well particularly when dealing with representations of sound. As others have said it makes it much easier to deal with amplification and attenuation because being a log scale subtractions can be used instead of divisions and additions instead of multiplication. The principle has been widely used in other areas of maths and was discovered long before electronics.

[fivefish]

When you need to convert a ratio of monetary values to dB, remember to use the factor x10, not x20, since money is power.

Hahaha... good one.

decibels were devised for audible sound and out ears are logaritmic in response,

No. The Bel was originally used for power measurement in telephony (named after Alexander Graham Bell).
decibel is one-tenth of a Bel. 

[IanB]

No. The Bel was originally used for power measurement in telephony (named after Alexander Graham Bell).
decibel is one-tenth of a Bel.

We use the decibel because the bel was too big for normal use. I guess that's because A.G. Bell was a bighead... 

[Simon]

No. The Bel was originally used for power measurement in telephony (named after Alexander Graham Bell).
decibel is one-tenth of a Bel.

We use the decibel because the bel was too big for normal use. I guess that's because A.G. Bell was a bighead... 

ok but isn't 1dB 1/10th of a Bell ?, as soon as we talk 10, 20 dB we might as well say 1B, 2B, but i suppose it also makes sense to keep it all in the same unit and use 1dB not 0.1B

[T3sl4co1l]

If you round down your decibels to the nearest multiple of 10, and express the rounding error as a linear (rather than logarithmic) factor, you have precisely the scientific notation.

Alternately, if you absorb the linear factor of scientific notation into the exponent, so that all numbers are represented as 1.0 x 10^p, you have exactly the decibel notation -- well, bels anyway, plus a few superfluous characters (we don't need the "1.0 x 10^" part, putting a dB at the end to remind us of the difference).

Tim

[IanB]

And rather curiously, even the "linear" part of a floating point number, the mantissa, is not actually linear.

For instance, suppose decimal numbers are to be represented to a precision of 2 significant figures. Then the range of values that can be represented to full two digit precision is from 1.0 x 10ⁿ to 9.9 x 10ⁿ.

However, a one digit change from 1.0 to 1.1 represents a difference of 10% [= (1.1 - 1.0) / 1.1], whereas a one digit change from 9.8 to 9.9 is only 1% [= (9.9 - 9.8 ) / 9.8]. The scale is quite non-linear.

Sure, you can add more digits, but the general non-linearity remains. For instance, 1.00000 to 1.00001 is 0.001%, whereas 9.99998 to 9.99999 is 0.0001%. It is still ten times more precise.

This is actually a good reason why computers should work in binary. For instance, going from 100000 to 100001 in binary is 3.1%, and going from 111110 to 111111 is 1.6%. The difference in representational precision only varies by a factor of 2 rather than a factor of 10. This means that binary values can cover the range of possible values for a given precision with a more even distribution.

[TimFox]

No, the mantissa is linear.  If your code gives constant ratios (such as 10%) for a given increment, then that code is geometric or exponential (same thing).  If the code gives constant increments for a given increment in the code, then that is linear.

[IanB]

No, the mantissa is linear.  If your code gives constant ratios (such as 10%) for a given increment, then that code is geometric or exponential (same thing).  If the code gives constant increments for a given increment in the code, then that is linear.

But it doesn't give constant increments in value for a constant increment in the code.

If I increment 9.9e01 by 1, I get 1.0e02, an increment of 1. If I increment 1.0e02 by 1, I get 1.0e02, an increment of 0. The smallest increment I can now make is 10, in going to 1.1e02.

Floating point representation is a quasi-geometric scale, but floating point binary is closer to truly geometric than floating point decimal.

So yes, linear is the wrong way to describe it, but in terms of even distribution of numbers there remains an advantage to binary.

[T3sl4co1l]

What you are talking about has nothing to do with the representational system and all to do with the distinction between arithmetic and geometric operations.  A geometric (proportional) operation has a scale-dependent arithmetic difference, and vice versa.  It doesn't matter what writing system is used to express numbers for either operation.

Tim

[dom0]

No, the mantissa is linear.  If your code gives constant ratios (such as 10%) for a given increment, then that code is geometric or exponential (same thing).  If the code gives constant increments for a given increment in the code, then that is linear.

But it doesn't give constant increments in value for a constant increment in the code.

If I increment 9.9e01 by 1, I get 1.0e02, an increment of 1. If I increment 1.0e02 by 1, I get 1.0e02, an increment of 0. The smallest increment I can now make is 10, in going to 1.1e02.

Floating point representation is a quasi-geometric scale, but floating point binary is closer to truly geometric than floating point decimal.

So yes, linear is the wrong way to describe it, but in terms of even distribution of numbers there remains an advantage to binary.

The mantissa is linear, but obviously the absolute step size depends on the exponent.

[electrolust]

This is actually a good reason why computers should work in binary. For instance, going from 100000 to 100001 in binary is 3.1%, and going from 111110 to 111111 is 1.6%. The difference in representational precision only varies by a factor of 2 rather than a factor of 10. This means that binary values can cover the range of possible values for a given precision with a more even distribution.

The difference from 01 to 10 is 100% though!!!

Representational precision?

I hope by now you understand the silliness of what you have said.

[IanB]

The difference from 01 to 10 is 100% though!!!

Representational precision?

I hope by now you understand the silliness of what you have said.

What I'm talking about is floating point wobble. It is addressed in computer science in relation to the possible error when values are represented as floating point quantities in machine computation. It can be found referenced, for example, in the IEEE-754 standard.

There is nothing silly about it at all.

This article gives a more technical and detailed explanation:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

[electrolust]

Ah, well indeed that's exactly right.  Arbitrary precision requires arbitrary space, so tradeoffs are made.

It has nothing to do with the number base.

[GNU_Ninja]

I bet if dBs didn't exist we would have ...

invented 'em