Numbering Systems

Decimal 165 = Binary 1010 0101 = Hexadecimal A5 (because 1010_b = A_h and 0101_b = 5_h).

Just as in decimal we count 8, 9, 10, 11, so in hex we count E, F, 10, 11 ... 1E, 1F, 20, 21

Hexadecimal is base 16, so there are 16 digits needed - 0 thru 9 is 10 and A thru F is 6, 10 + 6 = 16. There aren't any digits after F. A lower case h is often used after hex numbers and a d after decimal numbers to avoid confusion. To represent a number greater than 15d (Fh), 2 digits are used just as 2 digits are used to represent decimal numbers greater than 9, 11 for example.

Therefore,

31d = 1Fh (1*16+15)

32d = 20h

33d = 21h (2*16+1)

34d = 22h

35d = 23h (2*16 + 3)

Suggest you read http://en.wikipedia.org/wiki/Hexadecimal

Good luck

Hex is simply for conveniently representing groups of four binary digits.
Take your long binary number, chop it into groups of four bits and work out each group of four bits into a decimal number, if the decimal number is bigger than nine, you use the appropriate letter to avoid having two characters.
It's simply about convenience.
By using 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F we can keep one alphanumeric character to represent any four bits of binary.
And thus two hex digits can conveniently represent an 8 bit binary word.

E.G
1010 is equal to 8 plus 2, which is ten in decimal (which is two digits and thus confusing).
ten in decimal is equal to A in hex.
Hex is really for going for expressing binary, the decimal is just a red herring.

Del

Are you wondering about case? Whether to use upper or lower or mixed case in the way these numbers are written out?

If that's your question - I rather suspect you understand the number system itself and that your question is more one concerning notational conventions; is this the case? (no pun intended) - then typically what is done is to keep whatever case you pick. To wit:

10fa48b

or

10FA48B

either one. If you're, say, a tech writer, look at what your Tech Pubs dept is using already and stick with that. You said you're a student; what does your prof use? Your textbook/handouts?

Consistency is more the rule here. There are no hard-and-fast rules when it comes to writing these numbers out, just conventions.

Historically, the letters are upper-case because Teletype®s had only upper-case letters. They didn't print in lower case. Consequently, printed matter then and later kept the upper-case convention out of momentum. One of those "accident of birth" things.

For my part, I use upper case for another reason: sometimes when I cite a hexadecimal as the first item in an English sentence the uppercase works out naturally, as English sentences typically begin with an uppercase letter. That's just a personal choice, however. If you're working in an established context, best to stick with that.

Hope this helps.

I understand decimal (0--9) Binary (1--0), Octal( 0-77777), Hexadecimal (0-F)

Each integer in Hex has a different unique symbol when you exceed 9.

I also understand that you can represent any number in either system and that the various numbering systems are simply shorthand to represent a basic binary number ,so that you don't have to print a long stream of 1's and zero's.

Hex is Base 16--0--thru F,

So what is base 32: 0 thru U?

What would base 64 be for the number 33:

Would it be V?

Instead of using Hex21?

For example, Hex 1F24=500 decimal.

Or would you simply repeat the Hex System to get the value?If they do, it seems like a lot of typing when you reach the higher numbers when it could be simplified by a different symbol instead.

There is a gap in my understanding somewhere, and I may not be explaining my question very well.

Any help you can render will be much appreciated.

Hell is therapeutic?

You gotta read behind the lines lol.

They make you stand in line there?

No, they make us stand on our heads. Don't believe those TV adverts.

So, somewhere in our vast universe, there are probably creatures with only 2 "fingers" that naturally count in binary, creatures with 8 "fingers" where octal is the norm,and so on.

1 billion in hex would be 369ACA00.

Anyone want to tackle a Googleplex in hex?

Ancient Babylon used Base 60. Sentient millipedes?

No wonder they "Babbled".

Well, there are 360 degrees in a circle. Mariners use points. (they actually WERE pointy sticks on a nav board...) where we would get phrases like "four points off the larboard bow, head North by north east. Lets see..that would mean that they would be working in a base 16 system (I think) Clocks of course work in base 12 and base 60. Architectural story rods work in base 6 (studs per 8 foot span) or base 18 (bricks per 8 foot span) So really, number theory is fairly straightforward, and you can use pretty much ANY base you care to choose. Whatever is suitable for your operation.

Once I figured out that base ten is as arbitrary as any other system, a whole new world opened up to me. Personally, I am partial to octal.

So in what system would a millipede have a thousand legs?

I still feel that due to my time in British schools between 1952 and 1973 gave me (and many others) the basis for learning counting in almost any format.

See also:-

http://en.wikipedia.org/wiki/Imperial_units

Firstly the coinage, in a Pound Sterling (at that time) was as follows:-

960 quarter pennies

480 Half pennies

240 Pennies, each one of them accurately cut enough to allow usage as weights.

80 Three penny pieces

40 Sixpences

20 Shillings

10 two shilling pieces - Florins

8 two and half shilling pieces - half crown.

4 Crowns

21 Shillings made one guinea.

We had similar things with weighing, Imperial:-

16 Ounces = one pound

14 Pounds = one Stone

2 Stones = one quarter

4 Quarters = one hundred weight (112 pounds)

20 Hundredweight = 1 Imperial Ton.

Then with distance:-

12 inches = one foot

3 feet = 1 yard

22 yards = one chain

10 chains = one Furlong

8 Furlongs = one Mile

3 Miles = one League

This only a small simple example.

But as you see, we had to be able to count in various bases, within the same things and to be able to convert from one to the other......good training for computer math.....

About 1969, I had to help a Yale Uni Professor pay his bill in a London restaurant......he could not figure it out!!!!

Great post! Fun.

It is amazing that, even now, a billion in Great Britain is different than a billion in the US. One could hope that at least that would be standardized.

The 10⁹ interpretation is pretty much universal* here, now.

*OK - maybe Britland isn't the whole universe - but it's certainly at the center!

Only the USA dances to a different mathematical tune as far as I am aware......

Its that old "NIH" problem.........

German Billion = 1.000.000.000.000

British Billion = 1,000,000,000,000

US Billion = 1,000,000,000

Look here:-

http://www.jimloy.com/math/billion.htm

The USA is different to most other countries!!! They should "join" the rest of the world!!!!

I always said you Guys could not count!!!!

Joke.

An American comes to a British Doctor in the UK.

American. "Doctor, I am married to a lovely English lady here and she wants longer/more sex with me."

Doctor. "And how often per night do you manage it at this time?"

American. "Between 1 and 3 times..."

Doctor. "That seems a reasonable number of times to me, but I can give you a book and some exercises to help further. Come back each morning and tell me how you did."

American. "Great Doctor, thanks."

Next Day. Doctor. "How many?"

American. "10 times Doctor, but she wants more!!!

Doctor. "Wow, can you?"

American. "Yes"

Next Day. Doctor. "How many?"

American. "20 times Doctor, but she wants more!!!"

Doctor."Wow, can you continue?"

American. "Yes"

Next Day. Doctor. "How many?"

American. "50 times Doctor, but she wants more!!!"

Next Day.Doctor."Wow, can you do that?"

American. "Yes"

Next Day. Doctor. "How many?"

American. "150 times Doctor, but she wants more!!!"

Next Day.Doctor."Wow, HOW can you do that? That is really amazing!!!!!"

American, swaying back and forth in time with his counts "Once, twice, three times........."

#74 is a veritable nexus of British Imperial Units. I love it!

Totally OT GA (hehe)

Q: So in what system would a millipede have a thousand legs?

Well, let's have a look: Hmm..not very promising. Seems there are 10,000 species of millipede covering 13 orders and 115 families (gosh..wonder if my ex is related...), so let's just cut to the chase and pick the bad boy of 'em all: Illacme plenipes. These blokes weigh in at a whopping 375 pairs. None have a thousand legs as far as we know. Still, I can't imagine buying shoes for them all, and you can forget pantyhose.

A: Base 9.0856(...).

You are confusing base number systems with modular arithmatic; anything that has repeating cycles or patterns. All of your numbers above are written in decimal base-10.

It doesn't matter, positional notation is only a way to help it to look "normal". Fact is, if I am counting laps of a race car, and find out that it is 85 seconds in one lap, 45 seconds in a second lap and 52 seconds per lap in the subsequent four laps, then I need to add in base 60 to determine how many minutes it takes to do the race.

When base number theory is presented in math class, the statement is made that ANY number base system can be used and they will give a few examples in an unusual base (i.e. 7, 3) to demonstrate that it is really possible and ensure that the student understands the concept.

In real life, where "practical" and "useful" are important terms, the only useful numbering systems are: 10=decimal, 2=binary, 8=octal, and 16=hexadecimal. That is it. I have never seen any others. The reason for these should be obvious but maybe not to everyone.

(10) Because we have ten fingers.

(2) Only important once computers were invented because that is how the memory works. (If someone invents a tri-state memory chip then a base-3 system would be useful.)

(8) This shortens the string of characters (3 bits) and still only uses one numeric digit without any special characters.

(16) This shortens the string of characters (4 bits) and only uses a few extra letters. Two hex digits represents a byte (8 bits, 0-255). Four hex digits represents a full word (16 bits, 0-65535). This is much shorter and easy for the human eye to detect changes.

Any number base higher than 16 is impractical because the number of characters required increases exponentially. English only has 26 letters and we generally do not count with those. Who would want to go higher?

The Babylonians?

This forum has led me to many areas in search of answers, and in my recent research, I have discovered:

There is a base 64 number system,using upper case alphabet and lower case alphabet characters, plus 2 other symbols, usually + and /, as shown in a link from #24 above.

There is also tristate logic that has been around for many years.

Bus Enable is the third state.

and then there is single sideband...

Now you are talking Ham radio or CB's.But there are now a multitude of broadcast methods,besides the old familiar am/fm,ssb.Digital being one of those.

In reality, digital transmission is still analog, it is just broken up into pieces of a certain sequence that are interpreted into data useable by the computer on the receiving end, which in turn transforms it into intelligible data for human consumption.And yes, everything inside every computer is still just one's and zeroes.(Unless you are talking about Quantum computers,that have an infinite number of states that exist between one and zero!).

Anything besides one or zero is simply there for our convenience.

Once upon a time all programming had to be done with single bits.

Programs were very small, and had to be well thought out and very compact.

As programs became larger, better ways of getting all of those one's and zeroes into the computer were developed, but still, memory was at a premium,and processor speed was very slow,so there was still a premium placed on efficiency and size of the program.

The various numbering systems are simply shorthand methods to these bits.

Now the evolution is at the stage where memory is virtually unlimited,speed is astronomical and GUI's have replaced the hard work of having to manually input every command. Just to construct an icon used to require many lines of code,with every bit position identified.At a certain level, this is still occurring,but we don't have to worry about it as a user.The programming guys, the ones that actually work with ones and zeroes, on machine level, that roll their brains in on a wheelbarrow every morning do that for us.

They are the guys in the trenches doing all of the grunt work, and modern society owes them a great debt for all of our modern conveniences.

There are programmers that use various programming languages to accomplish an assigned task,but they are using the tools made by the geniuses at machine level.

The emphasis on these programmers now is to "Get a working product out the door,and we will fix the bugs as they pop up."

Competition is a 61tch!

Hence all of the bugs in new software and the afterthought revisions.

I do not wish to stray too far from the original subject, so I'll stop while I am still on topic.

carries information. Just not digital information.

A remarkable invention in any case.

I understand SSB. Half of an rf carrier wave is wasted when it goes thru the detector diode .Someone decided to save a lot of bandwidth and power and only send one half of the normal signal,either upper or lower, thus doubling the number of channels.A great idea indeed, and it seems obvious and simple in retrospect, but that is the way of many great ideas."Gee,wish I had thought of that!"

We live in an analog world, and I prefer analog where possible,like vacuum tube amplifiers instead of digital solid state renderings of the same material.

The problem with digital in some cases, is the chopping up and reassembly of the original material, no matter how elaborate, is still not the same.The gaps may not be noticeable,but they are there nonetheless.Some numbers will not digitize to infinite accuracy,so an approximation must be made.It is easy to cut a pizza into 3 pieces, exactly equal, but it is not possible to represent 1/3 in decimal or binary exactly.The numbers are rounded off.This rounding off may not be significant after a certain number of decimal places, but the effect is a lack of ambiance,of true "reality".

The younger generation will not notice this, for they have no point of reference, and us old timers are fading away into the foggy mist of the past and will soon be just a photo on a wall, and our descendent grandkids kids will ask"Who was that?"

And they will reply "That was your great great great great grandfather.He lived in an analog world.They actually built things by hand back then, and walked outside in the sunlight.And there were flying things in the sky called birds,and things that were actually alive in the ocean, terrible monstrous things,before we learned how to control it for our purposes.And people actually ATE things that came from the water, they did not have universal food like we do.I can't remember his name though."

And so it goes, not always upward, but always onward.

Well put. I totally agree and gave you a GA to negate that OT, so you are back to 0 again.....

europium and Del have it. You're having trouble grasping 16 symbols (as would any of us), imagine 32 or 64! You are right that the main use for base16 is to make handling large binary numbers easier. A long time ago (yes I remember), octal was used to handle 3 bits at a time. I suppose that was to eliminate the need to agree on new symbols. But since all(?) computers used multiples of 4 (now 8) bits in the processors, hexadecimal came into general use. What took 3 octal digits can be expressed in 2 hexadecimal digits.

Yeah, but only Del got a GA.

Serves me right, I suppose (I knew I shoulda given the OP an example using Mersenne Primes )

1F24 is not 500 decimal !!!
500 decimal is

1 1111 0100 in binary

taking this as blocks of 4 as in my first post gives
0001 1111 0111 this becomes
1 F 7 in hex

I think you are guilty of overthink .
I once heard someone giving a huge ly complicated explanation and confusing a student.
The thing to realise is it's just done for convenience. Forget the decimal if possible and work between binary and hex or vice versa. Only convert to decimal if necessary.
Why? Because binary is what we use when actually use manipulation the bits in the electronics, driving ports turning things on and off etc. Hex is just a convenient way of writing binary.
Del

Um, I think it's 1F4h

1 * 256 = 256

15 * 16 = 240

4 * 1 = 4

256 + 240 + 4 = 500

I think something slipped in your comment between lines 3 and 5

Never mind - no point in beating a dead horsecat. One thing about this place - there's no point in checking your work, there's plenty of others going to do it anyway. Right?

I just miss-copied the binary which perfectly illustrates why we need hex!
thus with a swish of his cape Del turns disaster into triumph as scampers away unscathed
Del

Where'd you buy that Hex Inverter? I want one!

Guy called Schmitt's got some 7414's going cheap ...

Would that be that trigger-happy TTLator and counter-hex maestro Jacques Schmitt?

Or was it 'hex counter.' Do they come in six-packs? Counters, I mean.

I don't know Jaques Schmitt.

Or maybe I do. Double negatives are always tricky.

You are correct.That was a typo on my part,caused by fat fingers on slim keyboard.

It is interesting that they still use Hex when 64 bit computers are now the norm.

Admittedly,Hex is easy, once accustomed to it, but it looks like a longhand way to handle 64 bit numbers, especially if the number is really large.

Even handheld calculators can convert from binary to Hex to Decimal, etc.

Anyway, I yield to the powers that be, I am just a newbee, and , as someone said, guilty of "Overthink"

Never, ever think of yourself as "just a noobie." That's the worst thing you can do.

Think of yourself as "someone with a fresh pair of eyes."

There might be nothin' new under the sun, but I rather suspect most of it has yet to be seen - and only by unencumbered eyes.

"Seek the wisdom of the ages, but look at the world through the eyes of a child."
~ Ron Wild

1F24 Would equal 7972 in Decimal.

On the contrary mon ami, Hex is easy to change from 64 bit 1 & 0 to hex or decimal.

1010|0011| =8 bit

i normally us 2 to the power method if the most right is the LSB (Least Significant Bit)

that is 2 to the power 0 (=1) then the next one is 2 to the power 1 (=2) etcetera.

If you do all the 64bits like this it gets tedious, so just doing it in groups of 4 is more convenient.

so the right 4 bits

2³ 2² 2¹ 2⁰

0 0 1 1 = 2 + 1 =3 dec and 3 hex

left 4 bits

1 0 1 0 = 8 + 2 = 10 decimal and A hexadecimal

You lamented: "a typo on my part,caused by fat fingers on slim keyboard."

Not a problem. Think about it:

• Whole new and completely unforeseen branches of novel mathematics have been unwittingly spawned this way. For instance, 2 + 2 = 5 for very large values of 2. This fact would never have been discovered were it not for fat 'fingers on a slim keyboard'.
• Were it not for 'fat fingers on slim keyboard', millions of Facebook users wouldn't have any Friends at all,
• Microsoft writes most of their software that way (though I tend to suspect they prefer to use their thumbs). For instance, Windows was supposed to be called Panes In the Arse.
• My fingers are huge. Did you think my writing this post was an act of volition?

And so forth
You are a National Asset my friend!

I suggest that you try several test problems in base16 and base64. Use the same values but converted to the different systems, then you will see the advantage of having fewer characters to work with and keep a sense of value for.

111d x 150d = ?

Would you like to pay ABCDh for a sandwich or just Aa-64?

You seem to have a couple misunderstandings.

An integer is a number with no fractional part. 1 is an integer. 502 is an integer.
So when you write Each integer in Hex has a different unique symbol when you exceed 9, you should really write "Each digit in hex has a unique symbol: 1 through F."

The value of a digit in a particular place is consistent in numbering systems. Starting with the rightmost place, the value of that place is the digit times the base0. The next to the left is the digit times the base1, the next the base2, etc.
So 500d in hex is not 1F24. It is 1F4: (1 x 256) + (F x 16) + (4 x 1).

Large numbers in hex will always require fewer digits than the same number in decimal will.

Another convention you may see is Ox preceding hex numbers (instead of h after).

Base 32 and Base 64 are not generally used (but take a look at this.)

Ok ...
1F4 ... but I was close (ish)
It's hard to do counties with these paws.
Del

My polydactylic cat operates in base 6 or 12, depending on whether one or two feet!

Now we all know how a mime counts...

Yeah, but what comes after mime?

Revolution Mime?

Tem. (sigh)

THANKS! That explains it perfectly.I was on the right track, I just didn't know how to ask the question properly.

According to your link,: " Base 64 is also occasionally used in computing, using as digits "A-Z", "a-z", "0-9", plus two more characters, often "+" and "/".

I dunno 'bout that. I get...

0x7FEFFFFFFFFFFFFF = 1.7976931348623157 x 10³⁰⁸

Also if you are working with large numbers, don't sweat it, use your window calculator.

on start menu below click window start button.

In "search for programs and files" dialog box, type "Calc" you will see windows calculator link.

When calculator pops up, click view, and select "Scientific"

Type in dec # you want converted to hex, click "Hex" tick box to see, or click binary tic box, type in binary 1s and 0s #, click "Hex" tick box to see binary # converted to Hex. Etc.

I used to teach night courses in C and C++ programming to corporate weenies wanting to brush up on their skills. I absolutely forbade the use of calculators in class until I was satisfied my students understood what that calculator understood and why.

Your recommendation is good, and a time-saver for people who need it, but there's nothing like understanding what you're doing. Prematurely using a calculator in the learning process is crippling. I know, because I know kids who cannot fathom the concept of long-division on paper. My kids can take square roots on paper because dad's one of those Auld Skool types who insist on knowledge acquisition, not just learning something so they can regurgitate it on a TACS test. That's just animal training and dumbest damn thing ever to crawl out from under a rock, IMHO.

Gotta go. Gonna be late for my daily rabies shot lol. Take care.

I am working my way thru a digital instruction book, and I can now trace a keystroke from the key thru every gate to the display output, of a 7 segment display.The logic is simple, but when combined in the proper combinations,gives amazing results.

I realize this is very basic, but I am old school too, and I want to know from the ground up how stuff works.I have a long interesting road ahead.There is so much information available now!

I also bemoan the loss of effective teaching being replaced by rote learning,which is a sad commentary on parenting in our society, the non corporal punishment in schools and at home, and the emphasis on quotas instead of a real education being required to graduate.

Good. So now you can get started on something MUCH more interesting...

Boolean Algebra.

But before you go....

Grey Code

Try not to tear your hair out....

Interesting - I never knew about Gray Code. So it's not actually based on a "base" but rather on the mechanical limitations of switches. I have a vision of all digital electronic devices being driven to a state of chaotic breakdown and becoming suicidal when someone suggests switching to Gray Code to make things work faster.

The limitations of switches weren't quite the motive for developing Gray Codes. As only one bit changes state between any pair of adjacent symbols, Gray Codes are more robust codes in terms of signal-to-noise ratio than are other codes. Gray Codes are also handy if you want to minimize switching transients that may occur when, say, a whole gaggle of bits change state simultaneously, ie, from 0xFFFF to 0x0000 or vice versa, for example, in systems where such transients may introduce problems. Gray Codes are still used and not that much of a pain, really (IMO).

I am familiar with Grey Code, it is used in position resolvers for radar, among other things.It is called an ABSOLUTE encoder,versus a relative encoder.It generates a unique code for every position and is not affected by power loss,whereas a relative encoder simply generates the same pulse train constantly when in motion, and no signal when stopped.

I am studying Boolean Algebra now, and it is very interesting.A very convenient way to express binary circuitry.Just a matter of understanding the symbology and operands.

Rules.Rules.And more rules.Everything is rules.Learn the rules, you can play any game,and like any game, the more you play,the better you get.I hope to get into the amateur leagues with my pursuit of digital.I am still striking out more often than I hit,but I am getting better.

"Straight" binary could be used for an absolute rotary encoder, but it would be prone to errors when reading the position near a point where two or more bits changed value at the same position - the worst case being at the 360°/0° point, where the result changes from all 1s to all 0s. Due to slight variations in the mechanical alignment and electrical characteristics, the values read during the transition could be anything between all 1s and all 0s.

Gray code (note the spelling - named after Frank Gray) circumvents this by having only one bit change at a time, so the position is always read correct to the least significant bit (after conversion back to binary).

"'Straight' binary..." The Establishment's answer to Gay binary?

'Gray' Code is spelt with an 'r' right?

My mistake...that would of course be GRAY CODE, not "GREY CODE".

I love machine language....there are no vowels...grrr.

And yes, it is used on radars, and elevator systems, and things that make sounds like star trek sound effects. Its kind of fun to be adding (say angles) using gray code. I never mastered it...I always just converted them into standard numerical binary and did an end around carry (or whatever operation I needed to do) and then converted it back to gray code. Its really nice because there are, like NO transient spikes from counting up from (say) 7 to 8 ...binary would spike the power supply with this count, 0111 to 1000 and gray code would go from 0100 to 1100, (same thing of course)

You can get a converter here if you really want one.

Machine language you say?

AAC -Alter All Commands

AFVC -Add Finagle's Variable Constant

AGB -Add GarBage

AWP -Argue With Programmer

BB -Branch on Bug

BD -Branch to Data

BLP -Boot from Line Printer

CAF -Convert ASCII to Farsii

CCB -Consult Crystal Ball

CPB -Create Program Bug

CRASH -Continue Running After Stop or Halt

CU -Confuse User

DAB -Delete All Bugs

DBTP -Drop Back Ten and Punt

DBZ -Divide by Zero

DC -Divide and Conquer

DDS -Delaminate Disk Surface

DSUIT -Do Something Utterly, Indescribably Terrible

DWIT -Do What I'm Thinking

EBRS -Emit Burnt Resistor Smell

EDP -Emulate Debugged Program

ETI -Execute This Instruction

EWM -Enter Whimsy Mode

FPT -Fire Photon Torpedoes

FMP -Finish My Program

FRL -Fudge Result of Last operation

GCAR -Get Correct Answer Regardless

GDP -Grin Defiantly at Programmer

GREM -Generate Random Error Message

GSI -Generate Spurious Interrupts

GSO -Generate Stack Overflow

HELP -Type "No Help Available"

HHB -Halt and Hang Bus

HSC -Halt on System Crash

IAND -Illogical AND

IDI -Invoke Divine Intervention

IPI -Ignore Previous Instruction

IRPF -Infinite Recursive Page Fault

ISC -Insert Sarcastic Comments

JNL -Jump when programmer Not Looking

JRAN -Jump RANdom

JRL -Jump to Random Location

KCE -Kill Consultant on Error

KEPITU -Kill Every Process In The Universe

KSR -Keyboard Shift Right

LAP -Laugh At Programmer

LOAR -Log Off At Random

LOL -Laugh Out Loud

LRO -Lose Result of Operation

LWE -Load WhatEver

MAB -Melt Address Bus

MAN -Make Animal Noises

MAZ -Multiply Answer by Zero

MWAG -Make Wild-Assed Guess

NBC -Negate By Clearing

NIH -No Instruction Here

NMI -Negate Most Integers

NOP -Needlessly Omit Pointer

NPC -Normalize Program Counter

PUGH -Pack Up and Go Home (Unconditionally)

PUNT -PUNT (recursively)

RA -Randomize Address Register

RD -Randomize Data

RPSW -Randomize Program Status Word

RU -Recurse Unconditionally

SAI -Skip All Instructions

SFT -Stall For Time

SHABM -Shift a Bit More

SHB -Stop and Hang Bus

SIO -Scramble Instruction Order

SMR -Skip on Meaningless Result

SRBO -Set Random Bits to Ones

SRBZ -Set Random Bits to Zeroes

SRBI -Set Random Bits then Invert

TDRB -Test and Destroy Random Bits

TOS -Trash Operating System

TPONR -Turn Power Off for No apparent Reason

UAI -Use Alternate Instrucction set

UOP -Useless OPeration

UUBR -Use Undefined Base Register

VVM -Vaporize Virtual Memory

WBR -Wait then Branch Random

WF -Wait Forever

WP -Wake Programmer

WSWW -Work in Strange and Wonderous Ways

WUD -Work Until Demo

XIO -eXecute Invalid Opcode

XPSW -eXecute Program Status Word

YAU -Yell At User (synthesis plugin required)

ZAR -Zero Any Register

ZBR -Zero and Branch Random

ZEOW -Zero Every Other Word

ZPM -Zap Physical Memory

ZSR -Zero Stuff at Random

What are THOSE all about?

When I learned computing HEX didn't appear to exist. Probably because FFFF didn't "feel" like a memory location. Anyone remember 173000g or 773000G?

I am sure that you had all the answers you need, but I still feel, from your first question, that, maybe there is a point to clear:

At the start of the PC history, they used 8 bits registers, which is 8 binary digits, to address the memory. Up to date, 8 bits registers are used still. Also, the Hexadecimal representation was used from the begining.The biggest number (Positive integer that could be represented was 255 decimal (FF in hex). Therefore, 2 registers were used to get to the number 65536 (4 digits in hex, FFFF). This became the 16 bit PC. After that, you have the 4 registers PC which equals 32 bit and the 64 bit (8 register address) PC (the operating system must be designed to use these addresse).

All the above has nothing to do with the numbering system bases which is a mathematical exercise: Octal = base 8 (0 -- 7), 8 bit registers could use this base for representation, but is rarely used. Hexadecimal 16 (0 -- F) each 2 bits can be represented by one symbol. Higher number bases are used in speciality cases as shown by the link provided...

My contribution here is to make sure that you were not linking the 8 bits, 16 bits, 32 bits and 64 bits computer memory addressing schemes with the need to have different numbering bases to be able to use them.

I hope I did not misread you.

Mate;

You are confusing number BASE systems with computer "bit" binary operating systems.

There are no alpha-numeric chatacters after "F" in hexidecimal.

The values are: F, E, D, C, B, A, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 HEX and corespond to : 15, 14, 13, 12, 11, 10 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 Decimal

Hexidecimal is a BASE 16 numbering system that allows assignment of "weighted" values to each bit within a byte of binary DATA in a page frame of computer memory.

Binary system bits are used at the Transistor-Transistor-Logic (TTL) machine system level to execute transistor gate "ON" (1) and "OFF" - (0) that correspond with assigning the system weighted values (in this case BASE 16 value) to the respective memory addresses.

This allows logic function to be executed within the computer/machine by addition subtraction, multiplication, and division of the weighted values within the memory addresses being accessed by the programming.

A 32 bit system has eight (8) bytes with four (4) bits of binary.

A 64 bit system has sixteen (16) bytes with four (4) bits of binary.

This translates into the actual number of bits within a page frame that is available of access by the program per line/row entry.

Search this on wikipedia under number conversions for better understanding and also look at computer machine language for a better understanding of the 32 and 64 bit systems and their respective capability of program execution and machine configuration use.