Questions tagged [binary]
For questions about representing numbers in base 2 or performing arithmetic on them.
98
questions
1
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0answers
11 views
Is there a binary representation where the encoding distance grows with the arithmetic distance?
I need to binarily encode/decode small integers (around 10 bits), in such a way that the hamming distance of the encoded number grows monotonically with the (absolute value) arithmetic distance of the ...
1
vote
1answer
28 views
Create binary numbers with a described pattern
I am looking for an algorithm that can create numbers following certain patterns. Let's say I have a binary number of size n and the patterns I would like to create is having 0s and 1s in equal ...
1
vote
1answer
44 views
Assign few binary variables to make all polynomials identically zero
I have 50 polynomials $f_i$ over binary variables $(x_1,\ldots,x_{100})$. Also $f_i(0,0,\ldots,0)=0$
for any $i \in [1,50]$. I want to assign few variables so that all $f_i$ will be
identically zero. ...
3
votes
2answers
60 views
How do computers *really* work? (at the most basic level)
While learning about computers I will read about RAM and Storage and the CPU, and while these explain the architecture of a computer and how parts of a computer work together, I still don't understand ...
1
vote
1answer
59 views
How can you represent a Huffman-tree in Hex?
I was trying to store a Huffman tree in a binary file recently. I thought it wouldn't be a big problem since you actually have the binary codes already in front of you.
Well, the difference is that ...
-2
votes
0answers
17 views
Cache structure in a particular case
A memory unit consists of 64KB of main memory, 1 KB of cache memory organized in direct mapped cache the cache line consists of 16 bytes.
What is the size of address bus?
How many bits are required ...
1
vote
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 ...
0
votes
0answers
15 views
Binary 2's complement to decimal
I need to transform 2's complement from binary to decimal
The binary integer is 10001001
This is my thought process. Could someone validate my thought process or correct it, please?
...
1
vote
1answer
14 views
2's complement substraction
I need to perform 2's complement operations on -50 - -48
From a mathematical point of view the following would be true.
-50 + 48 = -2
If I would follow the steps I would have:
I got to this result by ...
0
votes
1answer
24 views
How can I tell if a bit pattern can represent offset gray-code?
I have a very poor understanding of gray code in general and I find it to be a difficult thing to learn. While trying to learn about it I stumbled upon this seemingly looking trivial question that I ...
-2
votes
1answer
23 views
Consider 4 positive integers a,b,c,d having exactly 10^11 bits (considering the leading zeroes) in the binary representations
Consider 4 positive integers a,b,c,d having exactly 10^11 bits (considering the leading zeroes) in the binary representations. Positions are numbered from 1 to 10^11. Every 3rd bit of a is equal to 1 ...
3
votes
1answer
77 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 ...
0
votes
1answer
32 views
is duality principle in boolean algebra is true for every expression
Let say A = 1 and B = 1
and then A+B = 1
now by using duality(replacing or gate by and gate and 1 by 0) we can say that, A.B = 0
but this is not 0, because 1.1 = 1, so please anyone clear my ...
0
votes
0answers
37 views
How did we go from Binary to something like Python?
If there's one thing the pandemic has shown us its that High school Geometry did not save us. I am a high school math teacher and I understand my job and its usefulness only exist in a post scarcity ...
1
vote
2answers
41 views
Simple question about signed integer multiplication
If you have a signed integer int x = any
And then state that x < 0
Is the following statement true or false?
...
0
votes
1answer
31 views
Probability of loss using a binary symmetric channel
Today we talked about Information Theory and the binary symetric channel.
For newbies here is a little explanation :
For instance if I want to send a binary to someone :
The bit will be "flipped&...
1
vote
1answer
72 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 ...
1
vote
2answers
55 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.
1
vote
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 ...
1
vote
1answer
28 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 ...
0
votes
0answers
42 views
Is $x$ in the working range [3,2]?
Consider $x$ = $(0.1001)_b$ and $F$[3,2]. ($F$[3,2] is the set of all floating point numbers with 3 digits in the mantissa and 2 digits in the exponent.)
The question is $x$ in the working range [3,2]?...
1
vote
1answer
51 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 ...
-1
votes
1answer
44 views
How does malware enter the computer and take control on a binary or machine code level?
Malware can enter a computer in various ways, but I would like to know how it is able to simply use 0's and 1's and machine code to take over a computer and how it can stay hidden from antivirus ...
0
votes
2answers
131 views
Binary subtraction with numbers in 2's complement
How can i perform binary subtraction of two numbers that are already in 2's complement?
I have to subtract 01010011 from 10100110,both numbers are in 2's complement.
I know that 10100110 is -90,and ...
2
votes
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)^...
0
votes
0answers
35 views
CNF encoding of additions
I have $m$ equations of the following form:
$$x_1+x_2+\cdots+x_n=s,$$
where each variable is either 1 or 0, and the total number of variables is $m\approx3{,}000$. So Iām thinking of modeling each ...
0
votes
1answer
43 views
XOR of three integers where each pair's XOR is the other integer
I have three positive integers, a, b, and c. I know that $a\oplus b\oplus c=0$, so I got that each pairwise xor has to be the other positive integer. $a\oplus b=c$, $b\oplus c=a$, and so on, but I can'...
1
vote
1answer
26 views
Where is the theory about “binary toggling games”?
Let us -- using parameters $M, N$ and $L$ --
create an ordered set of size $M$ of $N$-bit long vectors $V$ and initialize them randomly: $V_k[i] = b \sim Bin(n=1, p=0.5)\ \forall i \in
\{0\ ..\ N-1\}...
1
vote
1answer
71 views
Binary to ASCII using logical operations
I am learning Computer Architecture from Introduction to Computing Systems (2nd Edition) and am stuck on this question.
What operations can be used to convert the binary representation of 3 into ...
1
vote
1answer
24 views
binary representation of ip prefixes
How does an ip prefix
90.0.0.0/4
translate to
0101ā
in binary
and
10.0.0.0/2
to ...
2
votes
1answer
43 views
Sums of $2^{-l}$ that add to 1
Consider the following problem:
You are given a finite set of numbers $(l_k)_{k\in \{ 1, ..., n \}}$ such that $\sum_{k=1}^n2^{-l_k}<1$. Describe an algorithm to find a set $(l'_k)_{k\in \{ 1, .....
1
vote
1answer
111 views
Calculating direct sum of 2 binary numbers
If we have say,key=ā0110ā and š=ā1100ā, how will šākey mod 2 be calculated and what will be the answer equal to?
0
votes
2answers
62 views
What needs led to the implementation of ASCII codes?
Prior to ASCII existing, we already had at least four number systems, namely
Binary
Decimal
Octal
Hexadecimal
So what were the needs that lead to the ...
0
votes
1answer
87 views
Number of nodes of given height in binary heap
Show that there are at most $\lceil n/2^{h+1}\rceil$ nodes of height $h$ in any $n$-element binary heap.
How can I show this? Or, how can I prove this?
2
votes
3answers
114 views
Name of binary encoding scheme for integer numbers
I once found on Wikipedia a nice technique for encoding $k \in (2^{n-1}, 2^n)$ uniformly distributed integer numbers with less then $\log_2n$ average bits/symbol, thanks to a simple to compute ...
0
votes
3answers
594 views
Why the 127 encodings of ASCII needed to be extended to 256?
As you all know the ASCII chart needed to be extended from 127 encoding to 256, I can't really see why. Some google expert on Coursera said "We needed that because of the foreign languages".
I still ...
3
votes
3answers
200 views
What are some uses of the Thue-Morse sequence in computer science?
Note: I come from a mathematics background.
The Thue-Morse sequence $t_n$ is a binary sequence that takes the value $0$ at the positive integer $n$ if the number of $1$s in its binary expansion is ...
1
vote
0answers
33 views
relationship between binary numbers and binomial heaps
I understand that a binomial heap can be represented as binary numbers according to the degree of each tree but what exactly is the relationship between inserting a new node into the binomial heap and ...
1
vote
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 ...
0
votes
1answer
97 views
How much time (in hours) will it take to check if the number with 20 binary digits is the prime number?
How much time (in hours) will it take to check if the number with 20 binary digits is the prime number, in problem it's mentioned that for number with 10 digits it took 1 hour it's also said that the ...
1
vote
2answers
273 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 ...
1
vote
1answer
71 views
Convert scientific notation decimal number to binary
I'm given the number:
$$8.881784197001252 \cdot 10^{-16}$$
I know it is $2^{-50}$ but suppose I didn't know. I need to convert it to binary.
One way is to apply the school taught algorithm on the ...
0
votes
2answers
1k views
Minimum number of bits to represent negative number
Minimum number of bits required to represent $(+32)_{base10}$ and $(-32)_{base10}$ in signed two's compliment form?
My attempt:
32 = 0100000 ( 1st zero - sign bit as positive)
So to represent +32 we ...
0
votes
2answers
39 views
Fundamental motivation behind the use of bits and binary representation
This is a naive question, but what makes binary representation special from a theoretical standpoint and from the standpoint of information theory?
If for technical reasons building ternary computers ...
0
votes
2answers
126 views
How to convert 010111 to decimal using only odd numbered positions while still applying the correct positional exponent?
I am trying to understand what this question is asking in terms of conversion. I know how to convert binary to decimal and vice versa, but the method you need to use has me confused.
I need to ...
1
vote
1answer
30 views
What's the least signifcant bit of a mantissa system?
If Mantissa is a 1-dot-M fixed-point number whose most significant bit is always 1 then, how is the least significant bit calculated?
I know the least and most significant bit of the mantissa ...
5
votes
2answers
280 views
checking '<' for two binary numbers in a cnf-formula
I want to check whether a arbitrary binary number is less or equal to another binary number in a cnf-formula. I can already construct a formula, which is not in cnf:
Lets say n and m are two-digit ...
0
votes
0answers
106 views
Binary to Decimal Algorithm Explanation
I came across some code today for converting binary to decimal, and I realised that I don't fully understand how it works.
Here it is in Python:
...
2
votes
1answer
26 views
Why does going from 2's complement (in binary) to the positive value by completing to 1 then adding 1 work?
I'm studying Computer science and this has confused me for a long time since our professor didn't give any proof.
When changing from 2's complement to the positive value, we can go in reverse (by ...
0
votes
4answers
139 views
Is decimal number 8 represented as 3 bits or 4 bits in computer?
I was told by my professor that
"It takes c * ln(n) bits to store a number n, where ln() is base 2 and c is a constant."
Thus, to store a number 8, we need ln(8) = 3 bits(I think const c can be ...
