Questions tagged [binary]

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

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20 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 ...
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1answer
12 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 ...
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1answer
60 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 ...
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1answer
31 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 ...
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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 ...
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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? ...
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1answer
28 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&...
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1answer
54 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 ...
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2answers
49 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.
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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 ...
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1answer
23 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 ...
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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]?...
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1answer
44 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 ...
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1answer
40 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 ...
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2answers
90 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 ...
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1answer
40 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)^...
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30 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 I’m thinking of modeling each ...
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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'...
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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\}...
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1answer
61 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 ...
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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 ...
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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, .....
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1answer
86 views

Calculating direct sum of 2 binary numbers

If we have say,key=‘0110‘ and 𝑚=‘1100‘, how will 𝑚⊕key mod 2 be calculated and what will be the answer equal to?
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57 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 ...
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1answer
78 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?
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3answers
111 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 ...
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3answers
581 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 ...
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3answers
193 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 ...
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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 ...
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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 ...
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1answer
86 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 ...
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2answers
251 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 ...
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1answer
57 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 ...
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2answers
959 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 ...
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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 ...
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2answers
118 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 ...
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1answer
29 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 ...
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2answers
275 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 ...
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0answers
100 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: ...
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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 ...
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4answers
138 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 ...
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1answer
34 views

Conversion from octal numerical system to binary numerical system

I know that in order to convert a numeral in base-8 to a numeral in base-2 I can write each octal digit as a binary word of 3 bits. I know that 2^3 = 8 that is exactly the dimension of the base of ...
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0answers
54 views

Can we represent $\sqrt{2}$ exactly even with infinite bits in mantissa [closed]

Can we represent $\sqrt{2}$ exactly even with infinite bits in mantissa in floating point notation or otherwise. We actually have to prove this is not possible. But why can't we if we have infinite ...
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1answer
428 views

Binary representation of 129 when using 8bits for two's complement?

I have this confusion regarding binary representation of decimal value 129 (or even 128). If 8 bits are used to represent numbers when doing the two's complement, then we know that '00000000' to '...
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1answer
24 views

For signed integers, why don't representative the smallest number as all zeros in binary, and the largest as all ones?

I'm reading up on bitwise operators, complements, and two's complements, and I'm wondering why the lower limit of a range (aka lowest negative number) isn't all zeroes in binary, and the upper limit ...
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1answer
663 views

How do the bits of a certain emoji code for all the colors?

I am watching an introductory course on computer science. At one part, it starts talking about unicode and how the bits 11111011000000010. He states that that codes for a laughing/crying face emoji. ...
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1answer
118 views

Is is possible to determine if a given number is xor combination of some numbers?

I have been given a number Y which is ($a$ xor $b$ xor $c$ xor $d$ xor $e$ ) of some numbers ($a$,$b$,$c$,$d$,$e$) and another no X. Now i have to determine if X is a xor combination of ($a$,$b$,$c$,$...
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1answer
21 views

What are the sufficient conditions for weighted binary code to be self compliementary?

I was going through binary codes and found out that if the weighted binary code is self complimentary then it's weights addition will be equal to 9. Is the converse true? If not then what are the ...
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0answers
89 views

How does normalised floating point binary work with two's complement?

I'm doing AQA a-level computer science, and the specification for which states that: Exam questions on floating point numbers will use a format in which both the normalised mantissa and exponent are ...
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2answers
147 views

Float number to binary

I would like to convert 0,347 and 0,9828 to binary, how can I do that? I know that sucessive multiplication by 2 can do this, but this method seems very painful and even ineffective since the size of ...