base 10 so important in electronics ?why so

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CIR.VINIT

Joined Feb 26, 2016
11
plz,do you have any good explanation for

Q) Why base 10 is so important ,so famous,so applied ,so extensive use in logarithm? is this in nature?
base 10 is our own mathematical choice to understand nature or it is nature own choice to creation.
etc etc
 

GopherT

Joined Nov 23, 2012
8,012
plz,do you have any good explanation for

Q) Why base 10 is so important ,so famous,so applied ,so extensive use in logarithm? is this in nature?
base 10 is our own mathematical choice to understand nature or it is nature own choice to creation.
etc etc
Most of electronics developed around audio. Early in Audio history was Alexander Graham Bell who noticed the ear has a log-like response to audio power. The bases for components and log steps of component values all catered to thus effect. Even the decibel (bel) unit of measurement was named for Bell ( if I remember correctly).
 

Papabravo

Joined Feb 24, 2006
12,770
As you are no doubt aware ancient history has multiple examples of a choice for a number base. The Mayans, of Central America, use a base of 20 for their number system. The Babylonians used the sexigesimal system (base 60) which is still used today in navigation and timekeeping. Base 10 might derive from the use of the fingers of both hands for counting. Maybe the Mayans counted on their fingers and their toes. If there is a fundamental number base it is arguably base 2 or binary. We owe the digits 0 through 9 to the Arabs. Probably one of the most important contributions to civilization. It sure beats the hell out of Roman Numerals for doing arithmetic.

P.S. As an exercise, some classmates in junior high and I, tried doing multiplication and long division with Roman Numerals and it was a mightmare.
 

Papabravo

Joined Feb 24, 2006
12,770
Most of electronics developed around audio. Early in Audio history was Alexander Graham Bell who noticed the ear has a log-like response to audio power. The bases for components and log steps of component values all catered to thus effect. Even the decibel (bel) unit of measurement was named for Bell ( if I remember correctly).
Logarithms can apply to any base. 10 is not particularly favored, since we also use the octave in this regard.
 

Papabravo

Joined Feb 24, 2006
12,770
Octave is more used in frequency, decibel measures the power or voltage differences for each octave on frequency change.
Right. I'm just saying you can construct a logarithmic scale using octaves or decades. The choice of a base does not matter. I guess you could also argue the base e was the fundamental base for logarithms, which might surprise some people because it is a transcendental number. That is, it is a number that is not a root of any non-zero polynomial equation with rational coefficients.
 

Papabravo

Joined Feb 24, 2006
12,770
Ten is the common base of math. Because most mathematicians have ten fingers to count on.

One can use any base and get the same result.

Computers us base two, because they only have two fingers.
Really? Computers have fingers??!! I've been misinformed all this time!! Sheeeesh!
 

Papabravo

Joined Feb 24, 2006
12,770
Getting back to the original question about the importance of base 10 to electronics, I don't think it is. Since arithmetic in any number base produces identical results I don't think the choice of a base matters. Identical results means the underlying numbers are the same, even though the representation of those numbers will be different depending on the choice of a base. It is the case that binary scaling of things like angles can simplify calculations when fixed point operations can replace floating point operations.

https://en.wikipedia.org/wiki/Binary_scaling
 

MrSoftware

Joined Oct 29, 2013
1,666
Number base is all about convenience. base-10 is convenient for people because we have 10 fingers and 10 toes to count on. When working with digital computers we typically use binary (base-2) because they're built from transistors which represent only 2 states, on and off, so it's a direct correlation. But things in computers are often grouped into bytes (8-bits, or 8 binary digits) and so we use hex (base-16) to represent them, because 2 hex digits nicely represent 8-binary digits. For example, in computer land the most you can get from 1-byte (8-bits) is 255 in base 10, which is written 11111111 in binary. 512 in base 10 is written 1111111111111111. So you can see that using base-2 will get really messy really quick. So for computers we frequently use hex, or base-16. This works out great because 2 hex digits represent 8 binary digits, or 1-byte worth of data. So that 11111111 is written as FF in hex. So much easier! Plus when doing math, your 2 hex digits will roll over at the same time as your 8 binary digits, so that's convenient. For example, 11111111b + 1b = 100000000b. Written as hex, 0xFF + 0x1 = 0x100 (the 0x indicates hex).

So anyway, base is all about convenience.

Really? Computers have fingers??!! I've been misinformed all this time!! Sheeeesh!
This guy has 2 fingers and 2 toes!

 

GopherT

Joined Nov 23, 2012
8,012
Number base is all about convenience. base-10 is convenient for people because we have 10 fingers and 10 toes to count on. When working with digital computers we typically use binary (base-2) because they're built from transistors which represent only 2 states, on and off, so it's a direct correlation. But things in computers are often grouped into bytes (8-bits, or 8 binary digits) and so we use hex (base-16) to represent them, because 2 hex digits nicely represent 8-binary digits. For example, in computer land the most you can get from 1-byte (8-bits) is 255 in base 10, which is written 11111111 in binary. 512 in base 10 is written 1111111111111111. So you can see that using base-2 will get really messy really quick. So for computers we frequently use hex, or base-16. This works out great because 2 hex digits represent 8 binary digits, or 1-byte worth of data. So that 11111111 is written as FF in hex. So much easier! Plus when doing math, your 2 hex digits will roll over at the same time as your 8 binary digits, so that's convenient. For example, 11111111b + 1b = 100000000b. Written as hex, 0xFF + 0x1 = 0x100 (the 0x indicates hex).

So anyway, base is all about convenience.



This guy has 2 fingers and 2 toes!

Back to your original question - is this in nature? Yes, and no. Yes, in general, Logarithmic relationships appear to be are all over nature. No, because the things that happen in nature are really exponential growth and decay that are plotted on logarithmic graph paper or logrithmicly divided inputs are used to make the effect appear linear. People have a really difficult time visualizing the differentce in log equations (including me) so it is much easier to plot them in such a way to make them appear linear on Log graph paper, or select log-spaced components to make what seems like a linear response (e.g. turning a log-tapered potentiometer double it's current distance from zero to make the sound seem twice as loud.

So, what are some examples? Bacterial growth (when nutrients and other stresses are not present) is exponential growth. Radioactive materials decay exponentially. When banks were offering an interest rate on savings account, comp0unded interest grows exponentially. The voltage of a capacitors charged or discharged through a resistor will increase or decrease at an exponential rate.

Anything with a first-order growth or decay will behave exponentially.
 

wayneh

Joined Sep 9, 2010
16,162
Anything with a first-order growth or decay will behave exponentially.
I agree, but this fact doesn't address why we favor base 10. I'm in the camp that we use base 10 because we use a base 10 counting system, probably because we have 10 fingers. If we had only 8 fingers, I'm pretty sure we'd grow up learning base 8. The elegance and beauty we see in nature would be viewed through a base 8 lens.
 

Kermit2

Joined Feb 5, 2010
4,163
I was taught that a number system base meant just two things.
How many single numerals can you write down before you have to add a second numeral to continue.
Base 10 - you can write 10 single digits, but must use two digits to count higher.
Base 2 - you can write 2 single digits, but must add a second one to count higher.

The numerical value of the largest possible single digit is always 1 less than the base.
 

MrSoftware

Joined Oct 29, 2013
1,666
Back to your original question - is this in nature? Yes, and no. Yes, in general, Logarithmic relationships appear to be are all over nature. ..... <snip>...
Yes, but you can perform log calculations using whatever number base you want and the result will be the same. Base is just the representation, the values would be identical.
 

GopherT

Joined Nov 23, 2012
8,012
I was taught that a number system base meant just two things.
How many single numerals can you write down before you have to add a second numeral to continue.
Base 10 - you can write 10 single digits, but must use two digits to count higher.
Base 2 - you can write 2 single digits, but must add a second one to count higher.

The numerical value of the largest possible single digit is always 1 less than the base.
That is true when you are talking about the base of the number system. But you can have base 2 logs or base 3.5 logs or base 10 logs all expressed in a base10 numbering system.
 

wayneh

Joined Sep 9, 2010
16,162
Ah yes, I see. I've been babysitting a 3-yr old the last couple days while his baby sister arrives. It's tough to do anything but skim while you keep one eye on the entropy-maximizer.

Nature does seem to produce a lot of log relationships. I'm pretty sure Newton developed calculus in part to deal with natural stuff. In other words he wasn't doing math for the sake of it, but needed a tool to fit, model and extrapolate natural relationships.
 
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