# Questions tagged [binary]

For questions about representing numbers in base 2 or performing arithmetic on them.

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5answers
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### Signed and unsigned numbers

How would the ALU in a microprocessor differentiate between a signed number, -7 that is denoted by 1111 and an unsigned number 15, also denoted by 1111?
3answers
2k views

### Shannon Entropy of 0.922, 3 Distinct Values

Given a string of values $AAAAAAAABC$, the Shannon Entropy in log base $2$ comes to $0.922$. From what I understand, in base $2$ the Shannon Entropy rounded up is the minimum number of bits ...
5answers
15k views

1answer
869 views

### Computing Hamming Distance Between Binary Vectors

Consider the following problem: Input: We are given a set $S$ of $n$ binary vectors. A binary vector is of the form $(b_0, b_1, ... b_n)$, where $b_i \in \{0, 1\}$. Therefore, there are $n$ vectors ...
1answer
96 views

### Greedy algorithm for subset sum on powers of 2

I have some $n$ numbers which are powers of $2$, say $a_1,a_2,a_3,\ldots,a_n$ which are not necessarily all distinct. I have option to give them any sign. I have to find if I can make their sum after ...
2answers
41 views

### How many unique counting functions there are for strings of N bits?

Let a counting function inc for inputs of N bits be defined as: ...
1answer
41 views

### Does a megabyte represent (2^8)^1000000 bits in base2? Isn't that more than enough combinations to represent everything?

Every introductory CompSci resource I can find goes through how 8 bits are in a byte, etc. So a byte can store some 2^8 values in binary. Then when asking about four bytes, we can assume this is (2^8)^...
1answer
43 views

1answer
38 views

### Given a binary tree $t$, prove that $size(t) < 2^{h(t)}$

I was able to prove that $size(t) \leq 2^{h(t)} - 1$ for any binary tree $t$, however I wasn't able to do anything reasonable with this statement. I know it's a proof by induction and that the ...
1answer
698 views

### Binary Floating Point Range/Precision for 4-bit Mantissa and 4-bit Exponent

I'm trying to understand binary floating point and using just a 4-bit mantissa and a 4-bit exponent (both 2s compliment) to keep things simple. As far as I can tell, the largest denary number I can ...
1answer
169 views

### what does “vector” mean in computer science?

I am trying to understand how computers work under the hood, and I came across following sentence. "Computer technology is based on electronic circuits able to process vectors of 0's and 1's. For ...
1answer
48 views

### Converting a 32-bit bit pattern into floating point number

In The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. i have read something like that, Single precision or 32-bit floating point forms the floating point number,...
3answers
27 views

### Negative Numbers in 32 bit Floating Point IEEE Numbers

So I understand the logic behind converting positive decimal numbers to IEEE 32 bit floating numbers but I'm not completely sure behind the negative one's. If for example we have a decimal number say -...
1answer
25 views

### Where does the decimal to binary “Divide by 2” algorithm come from?

I don't know if this board would be an appropriate place for this question, but I have been trying to figure out how the divide-by-2 decimal to binary conversion trick works: in which you divide the ...
1answer
91 views

### Converting Decimal Numbers between 0 and 1 to Binary

I've been playing around with a program I wrote that converts decimal numbers to binary numbers and i've noticed that eventually, after applying the algorithm (multiply by 2, subtract 1 if greater ...
2answers
56 views

### Is a file a string of zeros and ones?

Is a computer file just a string of zeroes and ones? If so, can it start with zeroes? I have not been able to find an answer, surprisingly.
1answer
18 views

### Conversion of fractional part of a hexadecimal number to binary

The Number is given as : (C012.25)Hexadecimal I have to convert it into octal . So I converted it into Binary First and got the result as : 1100000000010010.01000000 (Since each bit in hexadecimal ...
1answer
34 views

### 2d cellular automata Wolfram binary codes

This is a similar question to How 2d cellular automata rules works? However, the answer there did not provide me what I am looking for. Specifically, I want to be able to render these 2d cellular ...
1answer
53 views

### How does computer memory store the file name?

I have this doubt for long time. When i save a notepad file, it takes the memory for the information in the file. let's say, I type 'ABC' in notepad and saved the filename as stack, it shows that the ...
1answer
24 views

### binary representation of ip prefixes

How does an ip prefix 90.0.0.0/4 translate to 0101∗ in binary and 10.0.0.0/2 to ...
2answers
305 views

### Converting IPV4 address into Binary

So given an IP address it is converted into binary via calculating the binary of all different segments and then joining them. For example, 12.32.18.01 converted into a binary it would amount to this ...