Is this possible to create with a finite state machine?
So like 101 is accepted because odd number of 0's
but 1001 is rejected because even 0's
11 is not accepted because 0 is even.
etc etc.
Yes and it's easy to do it with only two states representing even number of 0's and odd number of 0's respectively:
The accepted state is 2
Related
all strings which contains even number of 0s or even number of 1s. Here I am asking about 'or' not 'and'.
I have come up with this: (1*01*0)*|(0*10*1)* so far...but this seems wrong to me cause when you draw DFA for the above language you can even accept 111 or 000 too.
For zeros, allow for any number of pars of zeros with any number of leading non-zeros and separating non-zeros. And then allow for any trailing non-zeros. If the string does not match this pattern, it has an odd number of zeros.
(1*01*0)*1*
And to do it for zeros or ones, just copy with 1s instead and add it as an alternative to the whole thing.
(1*01*0)*1*|(0*10*1)*0*
Also, 111 and 000 both correctly satisfy the condition, because 111 has an even number of 0s and 000 has an even number of 1s. Examples that shouldn't work would be 1101 or 011100.
What is the best way to check for minimum precision with numbers in SQL with Oracle database?
CreditCardNumber NUMBER(16) NOT NULL
CHECK (CreditCardNumber LIKE '________________')
or
CreditCardNumber NUMBER(16) NOT NULL
CHECK (REGEXP_LIKE(CreditCardNumber, '^\d{16}'))
I understand this is presentation level checking but I heard it's still good practice to avoid illogical data on the database level.
None of your function really work as expected as you will end-up having an implicit number to string conversion. Losing leading zeros. Maybe this is not a problem in that particular case, assuming a credit card number never start with a leading zero (and never will ? — according to ISO/IEC 7812 the leading number could be a 0 in some corner cases).
However, notice you don't have any benefit here in using the NUMBER type, as you will never perform calculation on the credit card "number". So, for that kind of data (credit card "numbers, telephone "numbers", zip codes, ...), I would strongly suggest you to use a character type (VARCHAR2 or CHAR if you prefer) instead, and at the very least check using an appropriate regexp than only digits are part of the string. Would be better to validate the checksum as suggested by #Allan in his answer though.
In addition, even if 16 digits is the most common case, bank card numbers are variable length -- from 12 to 19 digits (according to http://www.watersprings.org/pub/id/draft-eastlake-card-map-08.txt as I don't have access to the ISO official document).
Finally, concerning credit card numbers, you have to remember that depending your local regulation you are not necessarily allowed to store them unencrypted...
NUMBER(16) will only allow integers (i.e. if you try to insert '10.1', it will round to '10').
Keep in mind too that credit card numbers aren't always 16 digits - American Express uses 15.
The only benefit you'll gain from storing credit cards numbers in the NUMBER type is storage space. Since the digits are packed at a ratio of 9 digits to 4 bytes, 8 bytes will store 16 digits. However, every interaction with the data will require a type conversion to or from text, so you'll have to weigh the costs of storage, processing, and ease of coding.
The obvious way to validate that the value is wide enough is to check the value numerically:
CreditCardNumber NUMBER(16) NOT NULL
CHECK (CreditCardNumber >= 1000000000000000)
However, as #BenGrimm points out, this may not be valid for all credit card numbers.
One way to validate the card lenght per providers is to have a lookup table with each provider that you accept and the length of their card numbers. Again, you'd have to use a trigger to check against that, but it would allow you to verify that the length is appropriate is precisely correct.
A better validation might be to implement the Luhn algorithm in a function and use it to validate the column value via a trigger.
Finally, to reiterate what Sylvain Leroux pointed out, this should all be academic. You shouldn't be storing credit card numbers in plain text and may even be legally or contractually prevented from doing so.
You could potentially use ceiling(log10(Number)) = 16. I think for a credit card number there are better ways to check though.
I came across the follow question while reading a CS book, can someone please explain it to me? >"The Little Man computer can have ten operation codes (0-9) and address 100 words of storage (0-99). If binary numbers are to replace decimal numbers, what must the minimum number of bits in each word of the LMC be?"
Since you need to be able to distinguish 10 codes for operation, the minimum word size would have to be 4 bits. Using 4 bits, you can represent up to 2^4 = 16 possible codes (since each bit can be 0 or 1). Anything less (2^3 = 8) will not allow a separate binary number for each code.
The Little Man Computer is an architecture where one instruction is held in one word, therefore a word has to contain both the op code and the address. That means you have to hold 000 to 999 so my answer would be 10 bits. You could assume that the question implies the op code and address in separate fields - in that case you need 4 bits for the op code and 7 bits for the address making 11 in total.
Note that the LMC has a "jump if greater than or equal to zero" instruction and for this to mean anything you must be able to represent negative numbers - so that implies that memory has a sign bit. My own simulation allows -999 to +999 as numbers in memory.
I am working on a school project (if you couldn't figure that out just by the fact that I'm using MIPS and QTSpim), and my group chose to make a calculator for large (128-bit) numbers. We know how to do operations on 128-bit numbers, but what we're having trouble with is having the user input.
The professor doesn't quite know how to do it, so does anyone know if there is a way to load a 128-bit integer using MIPS and QTSpim?
MIPS registers hold 32-bit integers, so the result would have to be stored in 4 registers, but is there a way to make that happen?
Thanks!
I would:
Read the user input as a string
Convert the ASCII codes of the each digit to a number 0-9 (i.e. subtract '0')
Apply a radix conversion from base 10 to base 2, and hold the results in four 32 bit words
Why is there a difference between 8, 16, 32, 64, 128 bits? As gusbro described you validate the character string, for every new number character multipy by 10 and add the new number. You already mentioned you know how to do operations on 128 bit numbers so...just do the operations, multiply and add. If you dont know how to do the operations then you are mulitplying by 10 which 0xA which is 0b1010. Using elementary school math, starting with the ones column 0 times anything is zero. the base to the power 1 column (10s in elementary school the twos column here) 1 times anything is itself but you move over one location. the fours column is a zero, the eights column is a 1 so add in abcd shifted left three columns
abcd
x1010
=====
0000
abcdx
0000xx
abcdxxx
So multiplying by 10 is the same as taking the number shifted left one plus the number shifted left three, shifting and adding an infinite number of bits using 32 bit registers is fairly easy. If need be do it 16 or 24 bits at a time leaving bit 17 or bit 24 as the carry bit.
if you dont have a way to multiply and add 128 bits you wont get very far with a 128 bit calculator, so perhaps the above was un necessary.
Well, it is a low-level question
Suppose I store a number (of course computer store number in binary format)
How can I print it in decimal format. It is obvious in high-level program, just print it and the library does it for you.
But how about in a very low-level situation where I don't have this library.
I can just tell what 'character' to output. How to convert the number into decimal characters?
I hope you understand my question. Thank You.
There are two ways of printing decimals - on CPUs with division/remainder instructions (modern CPUs are like that) and on CPUs where division is relatively slow (8-bit CPUs of 20+ years ago).
The first method is simple: int-divide the number by ten, and store the sequence of remainders in an array. Once you divided the number all the way to zero, start printing remainders starting from the back, adding the ASCII code of zero ('0') to each remainder.
The second method relies on the lookup table of powers of ten. You define an array of numbers like this:
int pow10 = {10000,1000,100,10,1}
Then you start with the largest power, and see if you can subtract it from the number at hand. If you can, keep subtracting it, and keep the count. Once you cannot subtract it without going negative, print the count plus the ASCII code of zero, and move on to the next smaller power of ten.
If integer, divide by ten, get both the result and the remainder. Repeat the process on the result until zero. The remainders will give you decimal digits from right to left. Add 48 for ASCII representation.
Basically, you want to tranform a number (stored in some arbitrary internal representation) into its decimal representation. You can do this with a few simple mathematical operations. Let's assume that we have a positive number, say 1234.
number mod 10 gives you a value between 0 and 9 (4 in our example), which you can map to a character¹. This is the rightmost digit.
Divide by 10, discarding the remainder (an operation commonly called "integer division"): 1234 → 123.
number mod 10 now yields 3, the second-to-rightmost digit.
continue until number is zero.
Footnotes:
¹ This can be done with a simple switch statement with 10 cases. Of course, if your character set has the characters 0..9 in consecutive order (like ASCII), '0' + number suffices.
It doesnt matter what the number system is, decimal, binary, octal. Say I have the decimal value 123 on a decimal computer, I would still need to convert that value to three characters to display them. Lets assume ASCII format. By looking at an ASCII table we know the answer we are looking for, 0x31,0x32,0x33.
If you divide 123 by 10 using integer math you get 12. Multiply 12*10 you get 120, the difference is 3, your least significant digit. we go back to the 12 and divide that by 10, giving a 1. 1 times 10 is 10, 12-10 is 2 our next digit. we take the 1 that is left over divide by 10 and get zero we know we are now done. the digits we found in order are 3, 2, 1. reverse the order 1, 2, 3. Add or OR 0x30 to each to convert them from integers to ascii.
change that to use a variable instead of 123 and use any numbering system you like so long as it has enough digits to do this kind of work
You can go the other way too, divide by 100...000, whatever the largest decimal you can store or intend to find, and work your way down. In this case the first non zero comes with a divide by 100 giving a 1. save the 1. 1 times 100 = 100, 123-100 = 23. now divide by 10, this gives a 2, save the 2, 2 times 10 is 20. 23 - 20 = 3. when you get to divide by 1 you are done save that value as your ones digit.
here is another given a number of seconds to convert to say hours and minutes and seconds, you can divide by 60, save the result a, subtract the original number - (a*60) giving your remainder which is seconds, save that. now take a and divide by 60, save that as b, this is your number of hours. subtract a - (b*60) this is the remainder which is minutes save that. done hours, minutes seconds. you can then divide the hours by 24 to get days if you want and days and then that by 7 if you want weeks.
A comment about divide instructions was brought up. Divides are very expensive and most processors do not have one. Expensive in that the divide, in a single clock, costs you gates and power. If you do the divide in many clocks you might as well just do a software divide and save the gates. Same reason most processors dont have an fpu, gates and power. (gates mean larger chips, more expensive chips, lower yield, etc). It is not a case of modern or old or 64 bit vs 8 bit or anything like that it is an engineering and business trade off. the 8088/86 has a divide with a remainder for example (it also has a bcd add). The gates/size if used might be better served than for a single instruction. Multiply falls into that category, not as bad but can be. If operand sizes are not done right you can make either instruction (family) not as useful to a programmer. Which brings up another point, I cant find the link right now but a way to avoid divides but convert from a number to a string of decimal digits is that you can multiply by .1 using fixed point. I also cant find the quote about real programmers not needing floating point related to keeping track of the decimal point yourself. its the slide rule vs calculator thing. I believe the link to the article on dividing by 10 using a multiply is somewhere on stack overflow.