I'm taking the Nand2Tetris course on Coursera, the one where we translate VM Bytecode to asm, and I'm a bit confused on how the sub opcode is supposed to work in Project 7.
Assuming I've got code that looks like this
push constant 5
push constant 7
sub
I'd expect the output to be 2, but its -2 instead.
7 was the last thing pushed onto the stack, and I'm assuming the first thing popped off it, but it wasn't the first "argument" to sub? Why is that?
This is just the way two-operand stack operations are defined to work. The way to visualize it is that the operator is moved between the two numbers.
This system also makes it much easier to convert from normal notation, since all you have to do is move the operators, not reorder the numbers.
For example, (1+2)/(4-3) becomes 12+43-/
I need to convert a decimal number to a base between 2 and 9 using Little Man Computer. How do I proceed?
I believe successive divisions are the best method. In my opinion, I must write a code which divides two numbers, then save the integer ratio for the next division, as well as all of the remainders in an array of indefinite size, but I've been struggling with the division code for hours now. I tried searching for a code which divides two numbers, but all the ones I tried have mistakes/don't work. I'm stuck at the easiest part of the problem, I can't imagine how I'm ever going to be able to write a self-modifying code which manages an array of ever-increasing line positions and backtracks through it at the end to extract all the remainders. I'm at a loss here, any help would be appreciated.
I have been designing a Delta-Sigma DAC and have run into confusion and despair over the handling of signed numbers in my (sigma)counters and (delta and Vref) comparators.
I have tried to employ signed 2's complement but the EDAcompiler doesn't seem to notice when I do it, its most likely my own mistake!
So basically my question is, how (in Verilog) do I represent negative numbers in a way that they can be used in counters (which can therefore count up and down)? I am aware that a counter register that will hold signed numbers must be declared reg signed [:0]
Thanks!
Gavin
Well I am not that clear on your question. Some compilers may not be able to handle signed registers directly since if I recall correctly it is a Verilog 2001 feature. But generally if you use digital logic that works with signed numbers you shouldn't have an issue. For example if you use an adder ip just mention that inputs are signed numbers. As for the simulator you can select the type of data you need, generally by selecting the register/value, right clicking on the waveform window and changing the type.
Finally if you have to create the logic yourself just use sign extension. so lets say you are working with 4 bit values
-5 would be 11111011 and 5 wold be 00000101. So you can see that for negative numbers the MSB is 1 and for positive its zero. Using this you can interpret the numbers in your code but just make sure that the size is bigger then what you want to use so no overflow occurs.
I need to calculate the number of 1's in a binary number, lets say 5, so 00001001 would be 2 or n=2. I am using MIPS. Best way to do this?
The best way to do this is to count them.
You can check if the least significant bit is set (a 1) by anding it with one. If you get a non-zero result, it was set, so you should increment a counter (that was originally initialised to zero of course).
You can shift all the bits of a value right by using logical shifty operators.
You can loop doing both those operations until your value ends up as zero. There are conditional branch instructions in most architectures.
Your task, then, is to find those instructions for MIPS and put them in the correct order :-)
In no particular order, I'd be looking into the following set of instructions: {andi, srl, beq, addi}, though there may be a few others you'll need.
When people talk about the use of "magic numbers" in computer programming, what do they mean?
Magic numbers are any number in your code that isn't immediately obvious to someone with very little knowledge.
For example, the following piece of code:
sz = sz + 729;
has a magic number in it and would be far better written as:
sz = sz + CAPACITY_INCREMENT;
Some extreme views state that you should never have any numbers in your code except -1, 0 and 1 but I prefer a somewhat less dogmatic view since I would instantly recognise 24, 1440, 86400, 3.1415, 2.71828 and 1.414 - it all depends on your knowledge.
However, even though I know there are 1440 minutes in a day, I would probably still use a MINS_PER_DAY identifier since it makes searching for them that much easier. Whose to say that the capacity increment mentioned above wouldn't also be 1440 and you end up changing the wrong value? This is especially true for the low numbers: the chance of dual use of 37197 is relatively low, the chance of using 5 for multiple things is pretty high.
Use of an identifier means that you wouldn't have to go through all your 700 source files and change 729 to 730 when the capacity increment changed. You could just change the one line:
#define CAPACITY_INCREMENT 729
to:
#define CAPACITY_INCREMENT 730
and recompile the lot.
Contrast this with magic constants which are the result of naive people thinking that just because they remove the actual numbers from their code, they can change:
x = x + 4;
to:
#define FOUR 4
x = x + FOUR;
That adds absolutely zero extra information to your code and is a total waste of time.
"magic numbers" are numbers that appear in statements like
if days == 365
Assuming you didn't know there were 365 days in a year, you'd find this statement meaningless. Thus, it's good practice to assign all "magic" numbers (numbers that have some kind of significance in your program) to a constant,
DAYS_IN_A_YEAR = 365
And from then on, compare to that instead. It's easier to read, and if the earth ever gets knocked out of alignment, and we gain an extra day... you can easily change it (other numbers might be more likely to change).
There's more than one meaning. The one given by most answers already (an arbitrary unnamed number) is a very common one, and the only thing I'll say about that is that some people go to the extreme of defining...
#define ZERO 0
#define ONE 1
If you do this, I will hunt you down and show no mercy.
Another kind of magic number, though, is used in file formats. It's just a value included as typically the first thing in the file which helps identify the file format, the version of the file format and/or the endian-ness of the particular file.
For example, you might have a magic number of 0x12345678. If you see that magic number, it's a fair guess you're seeing a file of the correct format. If you see, on the other hand, 0x78563412, it's a fair guess that you're seeing an endian-swapped version of the same file format.
The term "magic number" gets abused a bit, though, referring to almost anything that identifies a file format - including quite long ASCII strings in the header.
http://en.wikipedia.org/wiki/File_format#Magic_number
Wikipedia is your friend (Magic Number article)
Most of the answers so far have described a magic number as a constant that isn't self describing. Being a little bit of an "old-school" programmer myself, back in the day we described magic numbers as being any constant that is being assigned some special purpose that influences the behaviour of the code. For example, the number 999999 or MAX_INT or something else completely arbitrary.
The big problem with magic numbers is that their purpose can easily be forgotten, or the value used in another perfectly reasonable context.
As a crude and terribly contrived example:
while (int i != 99999)
{
DoSomeCleverCalculationBasedOnTheValueOf(i);
if (escapeConditionReached)
{
i = 99999;
}
}
The fact that a constant is used or not named isn't really the issue. In the case of my awful example, the value influences behaviour, but what if we need to change the value of "i" while looping?
Clearly in the example above, you don't NEED a magic number to exit the loop. You could replace it with a break statement, and that is the real issue with magic numbers, that they are a lazy approach to coding, and without fail can always be replaced by something less prone to either failure, or to losing meaning over time.
Anything that doesn't have a readily apparent meaning to anyone but the application itself.
if (foo == 3) {
// do something
} else if (foo == 4) {
// delete all users
}
Magic numbers are special value of certain variables which causes the program to behave in an special manner.
For example, a communication library might take a Timeout parameter and it can define the magic number "-1" for indicating infinite timeout.
The term magic number is usually used to describe some numeric constant in code. The number appears without any further description and thus its meaning is esoteric.
The use of magic numbers can be avoided by using named constants.
Using numbers in calculations other than 0 or 1 that aren't defined by some identifier or variable (which not only makes the number easy to change in several places by changing it in one place, but also makes it clear to the reader what the number is for).
In simple and true words, a magic number is a three-digit number, whose sum of the squares of the first two digits is equal to the third one.
Ex-202,
as, 2*2 + 0*0 = 2*2.
Now, WAP in java to accept an integer and print whether is a magic number or not.
It may seem a bit banal, but there IS at least one real magic number in every programming language.
0
I argue that it is THE magic wand to rule them all in virtually every programmer's quiver of magic wands.
FALSE is inevitably 0
TRUE is not(FALSE), but not necessarily 1! Could be -1 (0xFFFF)
NULL is inevitably 0 (the pointer)
And most compilers allow it unless their typechecking is utterly rabid.
0 is the base index of array elements, except in languages that are so antiquated that the base index is '1'. One can then conveniently code for(i = 0; i < 32; i++), and expect that 'i' will start at the base (0), and increment to, and stop at 32-1... the 32nd member of an array, or whatever.
0 is the end of many programming language strings. The "stop here" value.
0 is likewise built into the X86 instructions to 'move strings efficiently'. Saves many microseconds.
0 is often used by programmers to indicate that "nothing went wrong" in a routine's execution. It is the "not-an-exception" code value. One can use it to indicate the lack of thrown exceptions.
Zero is the answer most often given by programmers to the amount of work it would take to do something completely trivial, like change the color of the active cell to purple instead of bright pink. "Zero, man, just like zero!"
0 is the count of bugs in a program that we aspire to achieve. 0 exceptions unaccounted for, 0 loops unterminated, 0 recursion pathways that cannot be actually taken. 0 is the asymptote that we're trying to achieve in programming labor, girlfriend (or boyfriend) "issues", lousy restaurant experiences and general idiosyncracies of one's car.
Yes, 0 is a magic number indeed. FAR more magic than any other value. Nothing ... ahem, comes close.
rlynch#datalyser.com