Questions tagged [binary]
For questions about representing numbers in base 2 or performing arithmetic on them.
61
questions
0
votes
1answer
52 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
36 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
29 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
49 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 ...
0
votes
2answers
33 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
38 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
22 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
227 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
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0answers
38 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
22 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
3answers
92 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 ...
2
votes
1answer
29 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 ...
1
vote
0answers
50 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 ...
2
votes
1answer
142 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 '...
0
votes
1answer
23 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 ...
0
votes
1answer
70 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.
...
3
votes
1answer
101 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 ($a$,$b$,$c$,$...
2
votes
1answer
18 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 ...
0
votes
0answers
53 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 ...
0
votes
2answers
103 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 ...
0
votes
0answers
31 views
Converting a decimal to IEEE754 32-bit binary number
Convert 0.625 to IEEE754 32-bit binary number.
0.625 x 2 = 1.250
0.250 x 2 = 0.500
0.500 x 2 = 1.000
So,
...
0
votes
1answer
83 views
Why isn't it necessary to store an integer part of significant in IEEE754 floating point notation?
We see that there is a sign, exponent, and mantissa part for the notation. But, there is no location for the significant bit.
Why isn't it necessary to store an integer part of significant in IEEE754 ...
2
votes
1answer
62 views
Prove that the next multiple of 4 is obtained using the next formula
I was reading an assembly procedure that needed to align addresses on 4 bytes boundary for performance reasons so it has used the next statement that i formulated as a theorem to be proven.
Let $s$ ...
17
votes
5answers
3k views
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?
0
votes
1answer
67 views
How does operating system display decimal numbers which are stored as binary? [duplicate]
What kind of magic happen with bytes in memory?
0
votes
1answer
39 views
Storage in computers?
If i want to save something in a computer such as a number 1 that would be 001 but if i save 001 in a computer how would the computer know that 001 is 1. Should we first save the number 1 in memory ...
0
votes
0answers
36 views
Find maximal matching in tree in $O\left(\frac{n}{\log n}\right)$
As any tree can be described as a binary sequence ($i$-th bit is 0 if the edge goes down and 1 otherwise, every edge is travelled twice $-$ up and down, so such sequence's length is $2 |V| - 2$), any ...
0
votes
0answers
18 views
Convert polynomial generator to binary form for crc [duplicate]
i have the polynomial generator x^3 + x
To convert to binary and i am unsure of the steps to complete. Help on how to convert various polynomials to binary would be greatly appreciated and i do not ...
2
votes
2answers
192 views
Why does little endian apply to numbers and not to text strings?
The Portable Executable file format is the format that Windows EXE files use.
It is a binary format.
Numbers are in little endian form. Thus, the following hex represents the decimal number 256, not ...
1
vote
1answer
232 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 ...
0
votes
1answer
32 views
How to transform a Infinite decimal of $\frac{23}{6}$ into binary?
How to transform a decimal of $\frac{23}{6}$ into binary?
$\frac{23}{6}$ is equal to $3.83333\bar{33}$, where the digit $3$s are repeated forever.
I do know how to translate finite decimal into ...
2
votes
4answers
134 views
Binary 2s Compliment Applied Twice Gives Original - How?
At the moment the maths behind binary 2s compliment seems like voodoo to me.
If I take 0011 (+3) and "flip and add 1", I get 1101 (-3)
If I apply the same process to 1101, ("flip and add 1"), I get ...
2
votes
0answers
27 views
How can I optimise a 8b10b encoding for maximum alignment?
Imagine you encode an 8 bit symbol as a 10 bit symbol that is sent sequentially over a wire. The goal at the receiver is to detect the byte boundary.
Since there are 4 times more encoded symbols than ...
0
votes
0answers
75 views
Worst case lower bound of binary search
For the question below, it is asking to prove the lower bound on the worst case is log(n). I have no problem proving this and the solution makes 100% sense to me. However, there is a comment at the ...
2
votes
1answer
62 views
Two's complement general formula
In college, we've seen some general formulas to compute the decimal value a of a binary representation $a_{N-1} \dots a_2 a_1 a_0$ in two's complement, $N$ being the number of bits.
For $a \ge 0$ we'...
14
votes
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 ...
0
votes
1answer
38 views
Need help converting machine code
I would appreciate some help with this question.
The 32 bit numbers below represent a MIPS instruction. identify the different fields and state which instruction it is. give the assembler source code ...
3
votes
2answers
40 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:
...
0
votes
1answer
320 views
Bytes from integer using bitwise operators
So I am extremely confused with using bitwise shifts used to extract the bytes from an integer. I find that if I do something like this...
...
2
votes
1answer
196 views
What exactly is a “binary file”?
I suspect this may be more of a concept / theory question, but, I haven't been able to wrap my brain around what exactly a binary file is.
I've read links such as the below:
https://en.wikipedia.org/...
5
votes
0answers
121 views
Partitioning through block moves to the end
Suppose we have a binary string $s$. We wish to partition this string in a series of $0$s followed by $1$s (alternatively: we wish to sort), using only one operation: moving three consecutive elements ...
2
votes
1answer
2k views
Confusion in 2's complement of 00000000
I'm solving the end of the chapter problems of Morris Mano's Digital Design (4th Edition, if that's relevant). In one of the problems, it is asked to simply find the 1's and 2's complement of 00000000....
0
votes
0answers
38 views
Is this the right way to convert a negative floating point number in binary using two's complement method?
I'm a cs student and i've just started learning about binary arithmetic.I have to do this homework assignement to get prepared for exams..I'm having some trouble figuring out how to convert a negative ...
2
votes
0answers
30 views
If 2's complement is the best way to represent numbers in computers, why worry about BCD and other binary codes?
I'm studying Digital Logic and Design. And in the first chapter, there's all this information about various binary codes. I did some searching on youtube and found this awesome video - https://www....
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votes
1answer
32 views
How can the binary OR function be computed by a MOD3 gate of constant fan-in?
I've been working on a problem and in order to prove the bigger picture, I need to understand how a binary OR function can be computed by a constant fan-in MOD3 gate. I would seem that the output ...
1
vote
1answer
104 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 ...
5
votes
1answer
157 views
Could a standardized ternary system be more efficient than the binary system? [duplicate]
Could a standardized ternary (base-3) system be more efficient than the binary (base-2) system? Binary is efficient for processing using logic gates, but can be bulky when using for file storage or ...
2
votes
2answers
162 views
0
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2answers
281 views
Fast searching through bitarray?
I've been thinking for some time but can't figure a way out.
I have big bitarray i.e. 1000+ items of 10_000 bits strings, I'm searching them now linearly. (currently it is stored in one chunk of ...
2
votes
1answer
245 views
Binary code and Hamming distance
I'm learning about CRC and Hamming distance and I have three questions.
Lets say we have binary code described by ($+$ refers to sum modulo $2$):
\begin{alignat*}{1}
a_1 &+ a_2 &+ a_3 &+ ...
