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Count Zero

Had we started indexing minutes at 0 instead, the "27th minute" would more logically be — Of course, both of these ignore the additional confusion that the 90th minute is sometimes considered to be — There are many answers but I miss an attempt to make it short and comprehensible for non programmers. I don't really want to be explaining memory addresses to a new programmer who doesn't understand memory layout and maybe doesn't even understand arrays yet. A simple and short example.

We have a list of elements aligned one after the other. The start of this list, the first element is flagged with a pin. To get the first element, we go to where the pin is.

To get the second element, we need to go to the pin plus one element. Starting at zero the computer can simply calculate where to go from the start location. More thoughts on that. Counting starts with "one" for the first element. Even for programmers.


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But programmers don't count elements when they start at zero, they give them names. These names start at the first number that can be built with digits. Zero denotes "nothing" but is the first valid number. I think it can't. The calculation described above is fundamental, the CPU does it like that. A compiler can't optimize necessary calculations away.


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  • Languages which start from 0 are currently popular but there are others which start from 1. These examples are quite old. Many of the start from 0 languages are derived from or inspired by C. Cobol is not fashionable now but it is still an important language in business and its arrays start at 1. RPG not role playing games also has arrays which start from 1. RPG is ugly and horrible but it is also popular in business. My Fortran is rather rusty but I think that it also started at 1. Very long ago, I used Algol and you could choose the starting index 0, 1, or even negative. For some applications, negative indexes e.

    I am not sure whether this was a standard feature or just one of the dialect that I used. Things were not so standardised back then. Let me delve into my personal experience from when I learned C in the mids.

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    It was a revelation on many levels: What C is a macro assembler with a few bells and whistles plus standard library , what a compiler does, under what constraints programming languages work, and why C was so fast. Why do you want to deprive your students of this insight? I think teaching arrays or any programming, really benefits tremendously from teaching memory addresses and some rudimentary assembler, so just go for it.

    All language abstraction is operating under the constraints of the metal. Your students will never understand why certain seemingly simple things are expensive or impossible if they don't know what they are actually doing. To sum up, essentially your third bullet point is the reason for the decision by the designers of C or probably rather, BCPL or B to start indexing at 0.

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    Saving a subtraction at each element access, i. True, today these original reasons are largely irrelevant; but today we have 45 years of code and a diverse C-rooted language tree.

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    Regarding these languages we are locked in for good. Having had the glimpse under the hood lets me actually appreciate the saftey, correctness and comfort provided by high-level languages and libraries. There are several explanations. But I would say that the main reason is because the number in computer science represents a memory offset i.

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    The technical answer, the one where you explain memory, and the base and index register, should be your preferred method of instructing. I understand that some people think it's daunting, but in reality, it is really straight forward, and it should be the first thing you teach about programming. All of the stack overflows, stack underflows, buffer overflows, null pointer exceptions, dangling pointers, memory leaks, etc are all a lot easier to understand if you start with the basics of what a computer actually does. And you don't need to get super-technical with buses and caches and so on, just enough so that when a memory-related problem happens, they will understand why it happened easier.

    Count from Zero to One Hundred

    As a comparison, which do we teach first in math: addition or multiplication? The reason why is because the latter is a concept built upon the foundation of the former. Teaching what a variable is before teaching what memory is akin to teaching multiplication without ever explaining addition. Everything we do in every computer language that exists on the market to today uses registers and memory. All of them. To completely gloss over the fundamental basics of computing is to perform a serious disservice to those you are supposed to be educating. I realize that many modern languages have done away with bare pointers because of their potential for misuse, but that means that the new generation of developers are growing up without understanding a critical part of computers.

    And pointers are still everywhere, just neatly tucked away behind references, objects, automatic variables, and so on. And that thing will be done by loading a memory address to a base register, loading an index register, and loading the data from memory as a result of the final calculation.

    If students do not learn this in class, they will certainly not learn it in the real world in any appreciable amount of time, and will write far inferior code for perhaps the rest of their developer career. Teach your students the basics of computers, and I can virtually guarantee that anyone with sufficient aptitude to be a developer to begin with will never ask the question "why do we count from zero.

    But in your PC you use an unsigned integer type as index set. So the problem is your number type. You could have a natural-number datatype without zero for your index and everything would be fine. Very simple: This is the offset of the address. So if an array called x is located with x at say 0x , an array that start's there has its first element x[first] at 0x By using:. Gypsy Spellweavers answer pretty much nails it, and looking at an index as an offset to a memory address as JosephDoggie and others suggest gives a precise technical reason.

    However, there is something I'd like to add:. It is a great tragedy that we don't "count" from zero in our everyday life. That is because early humans didn't have a concept of zero. That concept was unfortunately introduced much too late. We naturally use a decimal system because of our ten fingers we also use a base 5 system for stroked lists, with the diagonal stroke representing a thumb. We should actually use a base 11 system, because we can display not ten, but eleven states with our hands: 0 fingers up to 10 fingers up. So if only the concept of zero had evolved earlier in the history of mankind, "counting" from zero would feel perfectly natural to us and Matlab wouldn't start indexing at 1.

    Modern computer implementations physical, CMOS, as well as most virtual machines almost completely use only binary logic although some flash memories may use more than 2 states per physical bit cell. If that 1 bit addresses 2 bits of memory, then the two addresses are 0 and 1 to match the binary state nomenclature of the address bit.

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    Compositions of a small number of logic bits more than one are usually numerically interpreted as sums of powers of two times those binary bits, and the minimum unsigned sum is zero. Many early programming languages assembly grew out of shortcuts for data and program entry via binary switches. The conventions followed. Lots of binary zeros sum to numeric zero. And you count up starting from there. If you are a CS educator, you should not be teaching computation as magic, but as the result of the implementation of comprehendable binary logic. There is nothing in my register, there is one thing in my register, there are two things in my register.

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