Questions tagged [binary]

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

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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?
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 ...
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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 ...
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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 ...
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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: ...
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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)^...
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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 ...
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 ...
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 ...
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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,...
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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 -...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...