Questions related with (base 2) representation of numbers and their unique properties arising out of number representation.

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Upper limit for adding N numbers in grid of N processors in parallel

We must show how N binary numbers, each consisting of N bits each, can be added in a linear grid of N+logN processors. Suppose that the binary digits can be inserted directly in each processor of the ...
2
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4answers
769 views

Convert from base 10 to base 5

I am having a problem converting 727(base 10) to base 5. What is the algorithm to do it? I am getting the same number when doing so: $7*10^2 + 2*10^1+7*10^0 = 727$, nothing changes. Help me figure it ...
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3answers
110 views

Base 16 to base 10 number conversion

I know that if we want to convert from base 16 to base 10 we do as follows (for example): Given : $15C$ in base $16$ Conversion to base 10: $12 \times 16^0 + 5 \times 16^1 + 1 \times 16^2 = 348$ in ...
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2answers
23 views

Equal number of 1s and 0s in number of n digits

How many ways could one create a binary number of n digits where the number of 1s and 0s are equal? For example, if n was 8 then we could have: 10101010 or 11110000 In addition to this, I may ...
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0answers
12 views

how to write a lattice $[\alpha,\beta ]$ in the form [$a,b+c\omega _7$]

$\fbox{1}$ if we write [$2-\sqrt{7},5+3\sqrt{7}$] in the form [ $a,b+c\omega _7$],what is the value of $a,b,c$ $\omega=\sqrt{7}$,since $ 7\equiv 3\mod 4$ $N(2-\sqrt{7})=4-7=-3$ $N( ...
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2answers
58 views

Is there a name for the set of bit combinations of bitstrings?

Let $A \subset \{0,1\}^n$ be a set of $n$-bit bit vectors. Let me call a bit vector $b = (b^{(1)}, b^{(2)}, \dotsc, b^{(n)}) \in \{0,1\}^n$ a "bit combination" of the vectors in $A$ if: $$\forall i ...
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1answer
33 views

Number of Positive Definite Binary Matrices

How may positive definite matrices (over finite field- $F_p$) are possible? What is the criterion in getting those?
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2answers
75 views

What is the relation between this binary number with no two 1 side by side and fibonacci sequence?

I saw this pattern of binary numbers with constraints first number should be 1 , and two 1's cannot be side by side. Now as an example ...
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2answers
61 views

Probability of sum over a window of binary vector

I have a vector of one's and zero's of length n with a probability p of observing a one and 1-p of observing a zero. I slide a (overlapping) window of size $k$ across this vector and take the sum ...
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1answer
39 views

My Proof for the Cardinality of a Particular Binary Distribution

my question reads as follows: I have constructed a proof and am concerned about 2 things: 1) The validity of my proof. 2) The construction of my proof. I am asking for someone to read through ...
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1answer
34 views

Distance measures for binary data

I was wondering what are some good distance measures for binary data that have the following properties. I know that there are measures like the Jaccard index and the Dice Index, but they don't ...
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1answer
70 views

How many ways are there to arrange 1's and 0's with no two 1's in a row? [duplicate]

Given n spaces, how many ways are there to fill up the spaces with 1's and 0's such that no two 1's are together. For example, let's say n = 3 (_ _ _). There are 5 ways to fill up the spaces such ...
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1answer
34 views

Cubing a Minterm

I've just been going over some stuff I should actually already know - and I've come to a question that has really stumped me, (my math skill are lacking) and I don't actually know where to begin on ...
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1answer
36 views

Decimal to Binary

I am struggling to understand Decimal to Binary using the following method, given on the second last page of http://www.ling.ohio-state.edu/~scott/teaching/2008/spring/384/handouts/decimal-binary.pdf. ...
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1answer
23 views

Show that the following holds;

Let $h(p) = -p \log p-(1-p)\log (1-p)$ denote the binary entropy of a Bernoulli distribution when the probability of observing a zero is $p$, where $\log$ denotes the logarithm to base 2. Show, using ...
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1answer
387 views

Alien Abduction Brain Teaser [duplicate]

Okay Here is the brain teaser. 10 people have been abducted by aliens because they view them as being representative of the human race. They are going to test them to see if the human race is worthy ...
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0answers
79 views

Why doesn't this base 10 number x mod 2^y work for converting base 10 to binary

Okay I tried to convert 1 million to binary by dividing by a power of 2 and taking the remainder and dividing that by a power of 2 and so on and I got this: 1111010000100100000 Google says 1 million ...
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0answers
68 views

What is the result of the calculation: $8.375 - 0.375-0.875$?

Given the base $\beta=2$ (binary) and $t=4$ digits to represent the number in computer with hidden bit representation and symmetric rounding, what is the result of the calculation in floating point ...
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2answers
40 views

Convert from binary (with floating point) to decimal?

I have to convert the number (111011,01) in binary (2) to decimal (10). I looked up many guides on YouTube but none really explained how it's done, or it's very hard to hear. I would appreciate if ...
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1answer
54 views

What makes a floating point number finite?

We started studying about the binary floating point system, and talked mainly about the limitations when trying to represent fractions on computer systems, and how mostly what we get when manipulating ...
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3answers
47 views

How to borrow from zeroes in binary subtraction (no complements)b?

I know you can use complements to subtract, but I want to subtract these two binary numbers without that. I am unsure of how to borrow numbers from zero, check it out: 1000000 -101100 How do I ...
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1answer
22 views

Partioning Mystery

Who has the wisdom to answer the following: 9 distinct marbles distrubted into 4 distinct bags with each bag receiving at least 1 marble,how many ways can this be done? Thankyou for contributing! ...
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1answer
40 views

What's the proper way to subtract a negative number with two's complement?

Title says all. Is it just ordinary addition? Because that seems like it's too simple.
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0answers
44 views

Biased form with hidden bit

A computer stores a number of 16 bits word using floating-point arrangement. Given that the first bit is reserved for the sign and followed by 6 bits for the exponent using biased form. The remaining ...
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1answer
126 views

Time efficiency of brute force algorithm as a function of number of bits?

This is homework help so advising how to solve such a problem is appreciated. The question reads as follows: What is the time efficiency of the brute-force algorithm for computing $a^n$ as a ...
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1answer
58 views

Data Representation Question

A computer stores a number of $16$ bits word using floating-point arrangement. Given that the first bit is reserved for the sign and followed by $6$ bits for the exponent using biased form. The ...
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2answers
144 views

Binary Code Decimal (BCD)

I need help with the following question, my try is at the bottom: Question : Using Binary Code Decimal 8-4-2-1 representation, calculate 6789 + 7156 - 365 My Answer : 1101010000101 + 1101111110100 = ...
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1answer
58 views

Base change system

the people in aldeeran planet use a base six system. a]show how the aldeeran people represent each of the following: i) 291.5 (base 10) ii) 1010111 (base 2) iii) 71.6 (base 8) iv) 10A.4 (base 16) ...
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1answer
124 views

The maximum number of digits in binary multiplication

Given 2 binary numbers of n digits. (n can be from 1 to something large) What is the maximum number of digits of their product? I think it's 1 in 1-digit*1-digit, and 2n otherwise. But I want some ...
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0answers
87 views

conversion of number from base 10 to base 16

I have trouble finding an example of a conversion of a number from base 10 to base 16, where there is a loss of significant digits when using the Euclidean algorithm due to division by large numbers, ...
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2answers
2k views

Modulo 2 binary division (XOR not subtracting) method

I have attached an image showing a Modulo 2 binary division. I can roughly understand the working below which is using XOR calculation but I am not sure how the answer (in red) is being computed ...
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1answer
62 views

Find a decomposition and then an equation for the generating function for the class of rooted trees where each node has 0, 1, or 2 children.

Find a decomposition and then an equation for the generating function for the class of rooted trees where each node has 0, 1, or 2 children. how do you approach this problem?
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2answers
128 views

How do I calculate the binary form of a polynomial?

The 4 bytes used in CDROM sectors is just a usual 32 bit CRC. It uses the polynomial P(x) = (x^16 + x^15 + x^2 + 1).(x^16 + x^2 + x + 1) which expands to ...
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1answer
22 views

Continuous and binary variable question

For $y_1$ and $y_2$ as continuous variables how can this statement be reformed in binary and continuous variables with linear constraints Either $|y_1 - y_2| = 2$ or $|y_1 - y_2| = 4$
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1answer
78 views

How convert 1/2 to binary?

How convert 1/2 to binary? isn't it 0.1111 $1/2$ result $0$ $(1/2)*2=1$ result $0.1$ $2*2>1$ result $0.11 $ etc.
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1answer
74 views

Combinations or Permutations of bits

I am a computer science major and was explaining to someone how a computer uses bits to represent numbers. If you have 1 bit, you can have 0 or 1. With 2 bits, you can have 00, 01, 10, 11, or 0, 1, ...
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2answers
76 views

Mathematically get $n$th bit from integer

Most programming languages have functions for getting bits but I need to do it on a calculator so I need to understand how to do it mathematically. Basically I need a formula for getting the $n$th bit ...
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1answer
594 views

Formula for binary sequences of length m with no n consecutive 1s?

Formula for binary sequences of length $m$ with no $n$ consecutive $1$s? I know The number of binary strings of length $m$ without consecutive $1$s is the Fibonacci number $F_{m+2}$. But how about ...
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1answer
63 views

how do I assign -12 in base 10 to biased 32 in binary?

Not really sure how to approach this one. I understand how to convert decimal to hex and all that, but what is biased 32?
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1answer
61 views

Expressing as 1's complement

I have the problem: Express ( -43) as a word-length 1’s complement number 43 is in decimal. I understand how to convert to Hexadecimal and take the 2's ...
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1answer
278 views

Count number of binary relations between sets

He, I have following questions: We have sets $A$ and $B$, $\left | A \right | = m,\left | B \right | = n$. 1) How many binary relations are there from $A$ to $B$? 2) How many binary relations are ...
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0answers
1k views

Calculating minimum hamming distance of a code

We use hamming code of (7,4,3); Given 4 bits of information, we'll add 3 bits of parity, and one more parity bit for the 7-bits code. Given $x_3,x_5,x_6,x_7$ $x_1 = (x_3+x_5+x_7) \mod 2$ $x_2 = ...
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0answers
29 views

How to show that the spectral radius of a binary tree approaches exp(1) as the N tends to infinity?

How can I prove mathematically that the spectral radius of a binary tree approaches e as the number of nodes tends to infinity? I mean it is true that the increase in nodes number is exponential but ...
3
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0answers
92 views

Number of 'unique' one bit binary functions with N-bit inputs

Consider the set of binary functions that takes an N-bit input -> 1 bit output. There are 2^(2^N) elements in this set. Now potentially reduce this set by restricting to only considering functions ...
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1answer
47 views

Powers of 10 in binary expansion

I noticed an interesting pattern the other day. Let's take a look at the powers of 10 in binary: $10^0$ = 1 = 1 b $10^1$ = 10 = 10 10 b $10^2$ = 100 = 1100 100 b $10^3$ = 1000 = 111110 1000 b ...
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2answers
77 views

Binary concatenation

In decimal, I have the numbers 4 and 5 for example. I want to concatenate them into the number 45, but then in binary. In decimal, it's just a matter of sticking the numbers together, but I need to do ...
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3answers
161 views

How to fast convert from Octal to Hexadecimal

There has been a similar question before: How to convert a hexadecimal number to an octal number? But, in my case I need an Algorithm to directly convert a number from Octal to Hexadecimal and back ...
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1answer
29 views

Binary to Hexadecimal number

I know how to convert 0101 | 0111 in which the 0101 gives me 5, and ...
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1answer
68 views

Conditions for a decimal to be convertible to binary

All natural numbers (Base 10) can be converted to binary. No problem. But what about fractional numbers? All cannot be converted (finite expansion). Example: $0.625$ can be converted but $0.11231$ ...
3
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1answer
311 views

On a scale of 1 to 10, how likely is it that this question is using binary? [closed]

I just read this interesting xkcd strip: At first I thought it was funny, but as I got to ruminate a little over it, I was surprised to be unable to find an answer. As Karolis Juodelė pointed out, ...