Go Premium for a chance to win a PS4. Enter to Win


Formula to identify special binary numbers

Posted on 2013-02-06
Medium Priority
Last Modified: 2013-02-09
I need a formula that will tell me if a number, when converted to binary, has 1's with 0's between them.

Example -

00 = 00000000
01 = 00000001
02 = 00000010
03 = 00000011
04 = 00000100
05 = 00000101  *
06 = 00000110
07 = 00000111
08 = 00001000  
09 = 00001001  *
10 = 00001010  *
11 = 00001011  *
12 = 00001100
13 = 00001101  *

in the above binary representations, 5, 9, 10, 11, and 13 have 1's with one or more 0's between them so I would want a formula that returns true -

Example -
fncSpecialBinary(4) returns false
fncSpecialBinary(5) returns true


Question by:kevinvw1
LVL 53

Assisted Solution

Rgonzo1971 earned 400 total points
ID: 38863126

Basically, you should do your homework alone

Here is my pseudo-code
Diff = 0
Str = Dec2Bin(11)
for (int counter = 1; counter <= strlen(Str)-1; counter++)
    if Mid(Str, counter, 1) <> Mid(Str, counter + 1, 1)
If Diff >= 2
    Answer = True
    Answer = False

Open in new window

LVL 85

Expert Comment

ID: 38863204
int fncSpecialBinary(int n){
  int l,r;

Expert Comment

by:Marcos Freitas de Morais
ID: 38863257
All you need is a code to search the pattern: { 1, 0, ..., 1 } with a quantity of zeros varying from 1 to n.
Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

LVL 85

Accepted Solution

ozo earned 1600 total points
ID: 38863534
// further simplifying:
int fncSpecialBinary(int n){
   return ~n&-n&n>>1;

Author Comment

ID: 38864635
Rgonzo1971... nope, not my homework.  If your username is any indication of your age, I am older than you and have not been in school since the 80s.  :)
But since you went there...
Your answer works good for an Introduction to Programming 101 Junior college course.
But Ozo's answer is definitely Grad School material.

Expert Comment

by:Marcos Freitas de Morais
ID: 38865419
I thought about signed signed numbers, precisely ones' complement and I wanna post some comments about accepted solution.

If we use this algorithm by ones' complement for number 4, we have something like:
(~4 & 11 & 4>>1) // 11 is negative value to 4 and this sentece return true

Open in new window

To have a generic code, I wrote:
template<typename T>
int inline fncSpecialBinary(T n)
  int lsb = (sizeof(n)*8)-1;
  int rsb = lsb -1;

  while (-1 < rsb && ( /* 1st */ !(n&(1<<lsb)) || 
	               /* 2nd */ ((n&(1<<lsb)) && !(n&(1<<rsb))) || 
	               /* 3rd */ ((n&(1<<lsb)) && (n&(1<<rsb)) && 1 == (lsb - rsb))))
      if ( !(n&(1<<lsb)) || ((n&(1<<lsb)) && (n&(1<<lsb-1))))  

      rsb = !(n&(1<<lsb)) ? lsb - 1 : rsb - 1;
  return (-1 != rsb ? 1 : 0);

Open in new window

To call it,use:
std::wcout << (fncSpecialBinary<unsigned int>(num) ? L"TRUE" : L"FALSE") << std::endl;
// or
std::wcout << (fncSpecialBinary<unsigned short int>(short_number) ? L"TRUE" : L"FALSE") << std::endl;

Open in new window

LVL 36

Expert Comment

ID: 38866966

I think you are confusing your 'ones' and 'twos' complements. -n gives you the *twos* complement of n, ie. if n is 4 (and if we are talking 4-bit numbers as in your example) then -n is 12 (not 11)... and the result evaluates to false which is correct!

Expert Comment

by:Marcos Freitas de Morais
ID: 38867321

There is no mistakes. I have a x86 machine and for me the accepted solution works fine, too. Why ? My computer don´t use ones' complement to represent negative numbers.

But, if you get the code {... return ~n&-n&n>>1;...} and compile on computers that use ones' complement to represent their negative numbers, you'll get a bug. By the way, on that kind of machines -4 (decimal) == 1011 (binay) == 11 (unsigned decimal).

I just propose my code, because it's more portable one and to justify my comments.

I appreciate your attention.

LVL 85

Expert Comment

ID: 38870725
The C language standard does allow for ones complement or sign/magnitude representation, although I'm not familiar with any computer architecture that's used them since the 1960's
If you are running  on such a computer, you can use
unsigned int fncSpecialBinary(unsigned int n){
   return ~n&(~n+1)&n>>1;

Featured Post

Free Tool: ZipGrep

ZipGrep is a utility that can list and search zip (.war, .ear, .jar, etc) archives for text patterns, without the need to extract the archive's contents.

One of a set of tools we're offering as a way to say thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

In real business world data are crucial and sometimes data are shared among different information systems. Hence, an agreeable file transfer protocol need to be established.
Article by: evilrix
Looking for a way to avoid searching through large data sets for data that doesn't exist? A Bloom Filter might be what you need. This data structure is a probabilistic filter that allows you to avoid unnecessary searches when you know the data defin…
The goal of this video is to provide viewers with basic examples to understand how to create, access, and change arrays in the C programming language.
Introduction to Processes

972 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question