Questions tagged [binary]
For questions about representing numbers in base 2 or performing arithmetic on them.
0
votes
0answers
22 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
41 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
47 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 $s$ ...
16
votes
5answers
2k 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
45 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
37 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
26 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
8 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 ...
1
vote
2answers
72 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
21 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
64 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
13 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
19 views
IEEE-754 and machine numbers
I've been trying to wrap my head around machine numbers like the unit roundoff (u) and epsilon (e) in combination with the IEEE 754 standard. My textbook states some things that don't really make ...
0
votes
0answers
28 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
36 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
24 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
38 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
73 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
64 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
115 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
927 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
20 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....
-1
votes
1answer
30 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
56 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
100 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
145 views
0
votes
2answers
143 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
163 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 &+ ...
4
votes
3answers
1k views
Why does the formula 2n + 1 find the child node in a binary heap?
I learned that when you have a binary heap represented as a vector / list / array with indicies [0, 1, 2, 3, 4, 5, 6, 7, 8, ...] the indicies of the children of element at index n can be found with
$...
0
votes
1answer
301 views
0
votes
0answers
47 views
Avoiding overflow when comparing between 16-bit numbers
Let's say I have a 16-bit number system. and let $a, b$ a 16-bit numbers in this system.
I know that the numbers I can represent in this system are between $−32,768$ and $32,767$.
Let's say I want ...
4
votes
1answer
623 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 ...
1
vote
1answer
38 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,...
0
votes
1answer
318 views
Assembly language translation to machine code (process in “RAM”) [closed]
How does a assembler (at very basic level) work in translation of Assembly language to machine code ? Just want to know that what is happening in RAM ?
[What my understanding is that when when I ...
1
vote
1answer
132 views
n-bit 2's Complement Conversion
I'm learning 2's complement conversion for positional number systems. For the most part I have only seen 2's complement for represented in 8-bits. I had a discussion with a friend who explained that ...
8
votes
4answers
5k views
How can I multiply a binary representation by ten using logic gates?
So I’m currently working on something and I have converted all decimal digits 0-9 into binary.
But now I want to take say 6 in binary and increase its order of magnitude by base 10 (turning 6 into 60) ...
0
votes
0answers
121 views
As a number (base 10) approaches infinity, what would be longer? Represented in BCD or Base-2?
My professor asked this question in his lecture class and I can't figure out the answer.
My guess is BCD because you can't use up all the numbers (10 to 15), so you eat up space?
1
vote
0answers
124 views
Most efficient way to calculate log base 2
I recently started learning stuff with bits and now while I was solving one problem, I started thinking what is the most efficient way to calculate $$\lfloor \log_{2}K\rfloor$$
What I started ...
2
votes
0answers
134 views
K-ary tree that wrapped around
I'm not sure the best way to name this problem, but basically I need to construct a complete $k$-ary tree for $k \geq 2$ which has this nice property as $k=1$ tree that we can create a ring out of it.
...
