# Tagged Questions

Questions related with (base 2) representation of numbers and their unique properties arising out of number representation.

18 views

### Why should we subtract 1 to get maximum number in bits

I'm reading this article and it says that: This means that an unsigned INT can go up to $4,294,967,296$ (which is $2^{32}$ $– 1$). You need to subtract one because the result of $2^32$ starts ...
72 views

39 views

### What is the definition of binary sequence?

Can I write an infinite binary sequence like so: ...0111001001, ...10010 because I saw some people write infinite binary set from left to right like so: 1011000... , 101111... But I was not sure if ...
13 views

### pattern-sensible entropy measure

I have some binary images (meaning each pixel can be 0 or 1), I want to find a pattern-sensible entropy measure, which means for example that a chessboard should have a very low entropy value (almost ...
9k views

### How many 32 digit binary number combinations are possible?

How many 32 digit binary number combinations are possible? For example: $$00000000-00000000-00000000-00000000$$ $$00000000-00000000-00000000-00000001$$ $$00000000-00000000-00000000-00000010$$ $$.$$ ...
41 views

### Proof by Induction: Number of bit strings of length $n$ starting with a 1 or ending with a 0 [duplicate]

We showed that the number of bitstrings of length $n$ that begin with a 1 or end with a 0 (or both) is $3 \cdot 2^{n−2}$. Sketch a proof by induction for this. Would we prove this by ...
24 views

### nomenclature: binary prefix words and inverses

Are there any (formal or informal) words used describe the number/amount indicated by a binary prefix. For example, 3MV = 3 million volts. 3MiV = 3 [???] volts? Mimmilion? NOTE: Terms like this ...
119 views

### Binary counting problems

Recall that counting from 1 to n in binary takes $\Theta$(n) steps; i.e., the increment operation has constant amortized cost as opposed to $\Theta$(logn) in the worst-case. a) Analyze the amortized ...
42 views

### Bijection between $[0,1)$ and the space of binary sequences

My question deals with the problem of showing that the set $$\Omega = \{ \omega \colon \omega =(a_1,a_2, \ldots ), a_i =0,1\}$$ has the same cardinality as the interval $[0,1)$. In a textbook I read ...
25 views

### chi square for binary set

This should be fairly simple but I am having a difficulty understanding how the distribution tableworks. I am trying to make a java implementation of the chi-square function for binary data. I want ...
19 views

I have a funny radix conversion problem. I'm programming in a language called Solidity. It's very primitive and doesn't have many of the standard string and math operators that you'd expect in other ...
7 views

### Is it possible to write any binary string as the xor of a purposely choose subset of all the strings of the same length?

Given L to be the length of a string of zeros and ones, And defining f(n) as: If n is grater than zero f(n) is a string of length L, on which the first digit is one, followed by n-1 zeros, than a ...
24 views

### Binary string function with unique one-counting prefixes

I'm looking for a partial function $f$ from binary strings to natural numbers such that the following holds ($x$ and $y$ always represent binary strings, $\epsilon$ is the empty string, $H(x)$ is the ...
23 views

### Conditionals without use of binary variables

I would like a linear programming expression that has to satisfy certain criteria without the use of binary variables. i.e.: Let 0 <= B <= C However, if ...
479 views

### Longest sequence of 1s in binary representation of a number & Average Sequence length for number with N digits

I originally posted this to rec.puzzles in October 1992. I subsequently solved the problem (at least I think I did...) and published an article about it in early 1993. The article is nowhere to be ...
33 views

### list of all 256 binary combinations of 8 digits? [closed]

i don't have any coding/java etc software. how can i view all the 256 binary combinatios from 8 digits? can someone tell me where can i find them in a list (any site/online generator etc) or copy them ...
60 views

### Odd and even numbers in binary system

Actually here is a basic question, but i have a little problem about it. In binary system, for any number such as 1011001, can we say directly "it is end with 1, so it is an odd number"?, or firstly ...
Formula for binary sequences of length $m$ with no $n$ consecutive $1$s? I know The number of binary strings of length $m$ without consecutive $1$s is the Fibonacci number $F_{m+2}$. But how about ...