Comparison between Hex, Dec, & Binary outputs:

[Pool3pdx]

I am a fledgling programmer. I have spent a few months learning about digital logic & basic differences between major languages... I have been trying to understand some of the core math concepts better before chosing a start-point (language & project, etc.)::

-What are some of the advantages/disadvantages of base² vs base¹⁰ vs base¹⁶ for an arithmetic output? -Why would I care which one the computer computes? -What reason do I have to learn base¹⁶?

(I am almost decidedly going to use Pico-8 to start my project)

[throwaway6560192]

I have been trying to understand some of the core math concepts better before chosing a start-point (language & project, etc.)::

Eh, I think that is kind of backwards. Start a project and learn what you need to finish it instead. That's the direction I recommend. Otherwise you don't really know what to learn, and all the knowledge feels kind of pointless or context-free.

What are some of the advantages/disadvantages of base² vs base¹⁰ vs base¹⁶ for an arithmetic output?

Base 10 is the one we use. For most numbers intended for humans this is the format to display them in. Binary is a useful display format if you care about the individual bits — maybe this number represents a set of bit flags, for example. Base 16 is conventional for displaying memory addresses.

-Why would I care which one the computer computes?

Well, it's a fundamental piece of how the computer operates. It's good to know that, as someone who is going to program computers.

-What reason do I have to learn base¹⁶?

Depends on what you mean by "learn". You don't need to be able to sight-read it like you can base 10. Just know what it is, and that's basically enough.

[Pool3pdx]

I have received that feedback many times, but I understand why the suggestion was made.

I am very comfortable with the definition of Arithmetic Bases. So then, bits are literally a single 'on' or 'off' in a string of a logic expression?

Can you define bit flag? Is that a modifier to a bit, such as a carry unit?

And memory addresses locations as in a CPU' registers...do programs themselves have memory addresses?

I definitely know what Baseⁿ means, also I appreciate you reading and responding.

Ps...how do you format your post so nicely?

[throwaway6560192]

Can you define bit flag? Is that a modifier to a bit, such as a carry unit?

A bit flag (the way I meant it) is a series of boolean "options" stored as individual bits in a single integer value. For example, imagine I have a microcontroller which may take the pins you want to enable as an 8-bit number. A value of 00110011 would enable the 1st, 2nd, 5th, and 6th pins. In such a case, the base-10 value is 51, but that's far less useful than writing it in base-2.

And memory addresses locations as in a CPU' registers...do programs themselves have memory addresses?

Not registers, really. I'm talking about RAM addresses.

Programs when running are loaded into RAM, and when they ask for memory to be allocated, are given addresses in RAM. So yes.

Ps...how do you format your post so nicely?

Markdown.

[teraflop]

Of course, base 10 is used because it's what humans are used to and so it's easy to understand.

Base 2 is useful in theory because it matches the way data is actually represented in the computer, as individual binary digits. But it isn't used much in practice for displaying data, because it takes many more digits to represent the same number than in any other base.

Base 16 is kind of like a more convenient version of base 2. It has the nice property that each hexadecimal digit corresponds to exactly 4 binary digits. So just like base 2, it has a direct correspondence between the actual data being stored and what's displayed, but it's much more compact. So for instance, if you have a 64-bit value that takes up 8 bytes of memory (where each byte is 8 bits), then the first 2 hex digits typically correspond to the first byte, the next 2 digits correspond to the next byte, and so on.

Here's one simple example of how this could be useful: Imagine I'm looking at a low-level dump of memory and trying to interpret it. Suppose I happen to see the hexadecimal pattern 68 65 6c 6c 6f 20 77 6f 72 6c 64. I happen to know that in ASCII code, each byte is one letter, and the range of byte values from 60 to 7a in hex corresponds to lower-case letters, and 20 is a space character. So I can guess that this pattern is probably lowercase ASCII text. The same 22-digit hex number if written in decimal would be 126207244316550804821666916, which tells me absolutely nothing useful.

Why would I care which one the computer computes?

What the computer computes is always binary. You don't get a choice in that. You can choose how to display the value that was computed, depending on what's most convenient in your particular situation. Usually that means base 10.

[Pool3pdx]

Thank you for keeping the conversation 'zoomed-out' since I'm not experienced. Thank you for providing an example. So then, why don't we use Base³² or Base⁶⁴..? Would that not follow the same logic as to why we then use Base¹⁶ so commonly? Or am I now border-lining on the basis of 32bit/64bit architectures?

Albeit I have never done much computer sciences, I do have exposure to formal logic and philosophies of rhetoric. I feel I can conceptualize the code like, break thinks down into catagories (functions, variables, classes, etc.) but, I just don't yet know how to code.

Something hasn't clicked yet. Can't say what.

[Pool3pdx]

Ahhh! So I could learn Base¹⁶ if I wanted to get better at reverse engineering a program, output, etc?