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

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0
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1answer
33 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
82 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
367 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, ...
-1
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1answer
622 views

Inverse of binary matrix

I have tried creating an inverse of a binary matrix using the identity matrix method. Have an identity matrix alongside the square matrix and perform all the operations to convert the square matrix to ...
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3answers
77 views

converting to octal, hexadecimal and binary

Revising for an exam - could someone explain to me how you can convert an ordinary numbers to octal, hexadecimal and binary would be appreciated
4
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1answer
111 views

XOR of Three Integers

How would you prove the following: Given three non-negative integers $a, b, c$; if $a \oplus b \oplus c = 0$ then $(a - k) \oplus (b - k) \oplus (c - k) > 0$ for any $0 < k \leq min(a, b, c)$ ? ...
2
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1answer
83 views

Recurrence relations - simple questions, please verify my answers.

I'm posting this question because this is new material for me and I am unsure of my answers and have no one to consult with. I solved the first three and would appreciate feedback. I need help solving ...
0
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1answer
86 views

Compressing a short list of very large numbers?

Suppose that we are dealing with integers drawn from a random uniform distribution, on the range $[1 , 2^{30}]$. Is it possible to effectively compress a short list of random numbers, say $2^4$ ...
2
votes
4answers
356 views

Find the number of 1s or 0s in binary representation of a number

What is the number of 1s in the binary representation of $$3*512 + 7*64 + 5*8 + 3$$ Is there any shortcut for finding the number of 1s and 0s in a binary number which has been factored as above?
31
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10answers
4k views

In plain English, why does conversion from hexadecimal to binary work so cleanly?

Why does the trick of taking the binary representation of each digit and simply concatenating them work? e.g. 0x4E == 0100 ...
0
votes
2answers
162 views

Use strong induction to prove number of vertices on complete tree is $2l-1$

Can someone help me construct this proof using strong induction? Use strong induction on $l$ to show that for all $l \geq 1$, a full binary tree with $l$ leaves has $2l-1$ vertices total.
2
votes
1answer
118 views

Why do XOR and other operators on binary variables qualify as linear?

I never fully understood why is the operation $\oplus: \{0,1\}^n \times \{0,1\}^n \mapsto \{0,1\}^n$ considered linear ? I am well aware of the definition of linearity on real numbers, and I ...
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1answer
676 views

What is meaning of strict weak ordering in layman's term?

I gone through many pages using Google, but not understand exact meaning of Stick-weak Ordering term. I have this requirement while sorting strings. Thanks.
5
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1answer
358 views

Generating Function for Binary String Question

The following is an assignment question I have been trying to work out for quite some time. Let $C(x,y)=\sum_{n,k \geq 0} c_{n,k} x^{n} y^{k}$, where $c_{n,k}$ is the number of binary strings of ...
1
vote
1answer
711 views

Binary string with even and odd number of 1s [duplicate]

How could it be shown that the number of binary string of length k with an even number of 1s is the same as those with an odd number of 1s. Eg. for $k = 3$ : Binary string length 3 with even amount ...
1
vote
3answers
392 views

How to convert an infinite binary fraction into a decimal fraction

I am asked to write the infinite binary fraction $0.(1011)$, where the $1011$ is the repeating part, as a $\frac pq$ fraction. What are the steps to do this? EDIT: If $0.(1011)$ was in base 10, I ...
2
votes
1answer
45 views

Computation and Elimination (Solution Verification)

Consider a set B (of binary strings) given by the introduction rules: \begin{equation} \frac{}{\epsilon :B} \quad \frac{a:B}{s_{0}(a):B} \quad \frac{a:B}{s_{1}(a):B}\end{equation} ...
0
votes
1answer
113 views

Binary multiplication

Please don't be to harsh with me if you think that this is to simple, I just don't understand it. I been trying to follow this site(Method 2) to solve simple multiplication of $3 * 3 = 9$, but it ...
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vote
4answers
68 views

How do I convert from binary base to decimal?

I have a homework problem and I don't understand it. Here is the problem: The base two number 11111(base 2) has the same digit in all places. The same number can be written in different bases. Find ...
1
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2answers
121 views

Binary number theory

I want to know if there exists some book about "Binary number theory", I'm interesting in this because there many problems of ICPC about this topic. Thanks in advance
2
votes
1answer
72 views

Calculating 6 decimal digits of $3^{\sqrt2}$ using a calculator.

How can we calculate $3^{\sqrt2}$ to 6 decimal digits, using only a semi-basic calculator (Which has the square root too) and a pen and paper? I asked this question from my teacher and he ...
3
votes
1answer
106 views

Lower bound on a number theoretic function

Let $n$ be a positive odd integer, let $$n_j = \Bigl\{\frac{n}{2^{j+1}}\Bigr\}\,,$$ where $\{x\}$ denotes the fractional part of $x$, and finally let $k = \lceil \log_2 n\rceil$. Consider the ...
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2answers
354 views

converting decimals to base negative-10

I have a decimal (base $10$) number, $44$, and would like to convert it to base $-10$. I know how to convert $$ 164_{-10} \mapsto 44_{10}, $$ but not the other way around.
0
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1answer
47 views

Dyadic rationals representation in the computer memory.

So I know what a dyadic rational is and that is represented with a finite number of binary digits in memory. The idea is that I want an explanation why is it represented in this way ? Thank you.
0
votes
1answer
113 views

binary division and remainder

Q=A/B , Q is a real number expressed as a pair of 8 bits: most significant 8 bits for the integer part least significant 8 bits for the fractional part the number is unsigned for example: 0 0 1 ...
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2answers
52 views

Binary Numbers system for Programming

So, the maximum number 1 byte (8 bits) can have is 255, so does that mean 255 combinations of 0 & 1 in the 8 places?
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2answers
123 views

Arithmetic operation of binary numbers - Is my answer correct?

Does the arithmetic operation - 102 (base 10)- 39 (base 10), represented in 8-bit, when converted to binary have an overflow or underflow? My Ans - It has no problem. I mean there is neither ...
2
votes
2answers
364 views

Hexadecimal to Octal and Vice Versa

Convert Hexadecimal number to Octal - $(FD56.52A)_{16}$ to octal My answer - $(176526.2452)_8$ Convert Octal to Hexadecimal $(37.27)_8$ My answer - $(1F.5C)_{16}$. Correct or incorrect? Please ...
0
votes
1answer
88 views

Inserting values left to right in a binary search tree

What does it mean to build a binary search tree by inserting values from left to right starting from an empty tree? The "left to right" part confuses me..I know how to build one by normally inserting ...
2
votes
3answers
101 views

Finding element in binary representation of $GF(2^6)$

I got the following task: Let $F = GF(2^6 )$ be K[x] modulo the primitive polynomial $h(x) = 1 +x ^2 +x ^3 +x ^5 +x ^6$ , and let $\alpha$ be the class of x. I have a table with the binary ...
1
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1answer
161 views

running time of a multiplication algorithm

Here is a multiplication algorithm: given inputs x and y, add x to itself y - 1 times: z = 0 while y > 0: z = z + x y = y - 1 return z What is the running time of this algorithm? Is it ...
0
votes
1answer
56 views

consider the following subroutine, what is the running time

Suppose A(.) is a subroutine that takes as input a number in binary, and takes time O($n^2$), where n is the length (in bits) of the number. (a) Consider the following piece of code, which starts ...
0
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2answers
41 views

how long does this subroutine and loop take

Suppose A(.) is a subroutine that takes as input a number in binary, and takes linear time (that is, O(n), where n is the length (in bits) of the number). Consider the following piece of code, which ...
5
votes
1answer
180 views

Efficient division using binary math

I'm writing code for an FPGA and I need to divide a number by $1.024$. I could use floating and/or fixed point and instantiate a multiplier but I would like to see if I could do this multiplication ...
0
votes
2answers
89 views

Why the binary division of the two has the same quotent

I am trying to divide 110000 with 1101 in binary (long division). I use XOR each time. The divisions above should have quotent 100. However I might must misunderstood something. Could please anyone ...
0
votes
2answers
971 views

Arithmetic Overflow and Underflowing

I am a bit unclear about underflowing in terms of binary representation. Let's say that an unsigned 8-bit variable gets overflown from the addition of $150+150$. A signed 8-bit variable gets ...
0
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2answers
126 views

fill-in-the-blank induction proof

I'm stuck at homework task I'm working on. I would really appreciate some help. Here is the task: Let $f$ be a function on binary numbers defined recursively as follows. $f(0) = 1$ and ...
3
votes
2answers
164 views

Finite bit strings that do not contain '$00$'

I am studying for an exam and I am having trouble with this practice question: In this question, we consider finite bit strings that do not contain $00$. Examples of such bitstrings are $0101010101$ ...
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4answers
136 views

17539 decimal to binary not getting the same result

I'm trying to convert 17539 to binary. My math says its 110000010010001, but online calculators like this and this say it equals to 100010010000011. Who is making something wrong.
1
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4answers
638 views

How many bitstrings of length n contain an equal number of zeros and ones?

How many bitstrings of length n contain an equal number of zeros and ones? Progress Does $n!/2$ work as a solution since we know $n$ is even? For example, 000111 rearranged, $6!/2$? What ...
0
votes
2answers
702 views

creating a Binary tree based on a prefix expression

I want to find the value of a the prefix expression -/+8,10,2*3,2 and build its binary tree I am trying to learn this for a math course, but have absolutely no clue ...
3
votes
1answer
82 views

comparing bit lengths of binary numbers

Suppose I have two binary numbers x and y that have bit lengths of nx and ...
2
votes
2answers
175 views

Longest sequence of 1s in binary representation of a number & Average Sequence length for number with N digits

I originally posted this to rec.puzzles in October 1992. I subsequently solved the problem (at least I think I did...) and published an article about it in early 1993. The article is nowhere to be ...
0
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1answer
82 views

Implement a 1-bit adder.

The truth table is: A B Sum 0 0 0 0 1 1 1 0 1 1 1 0 So no carry. Is this correct?
1
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0answers
76 views

Probability of getting a Column full rank binary matrix

Suppose I have a $m \times n$ ($m>>n$) zero matrix (all of the elements are $0$). I want to flip $k$ ($k \ge n$ and can be controlled by the user) elements of the matrix randomly. After this ...
0
votes
2answers
137 views

Simplex and mathematical models: Truncating expresion to 0 if negative

Is there a simplex compatible way to model an expression that "truncates" (sorry for not finding a better word for it) the value to 0 if it turns negative? I have the following restrictions: ...
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5answers
87 views

Converting Hexadecimals

I need help converting Hexadecimals. How do I go about converting something like E0D base 16 to decimal? How about to binary?
1
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1answer
342 views

Binary relation composition (with itself)

To start off on the right foot. I've read: Relations (Binary) - Composition but I still can't really figure it out because those deal with finite sets. I have a infinite set: $R= \{(n,n+2)|n \in ...
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1answer
185 views

Complement Calculations - Why do I get different answers with ones' and twos' complement?

I am finishing an assignment related to complement calculations. The question is as follows: ...
0
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1answer
798 views

Add Hexadecimal that is in 2's complement.

Perform the following additions. The corresponding 16-bit binary numbers are in 2's complement notation. Provide your answers in hexadecimal. I'm not sure about this one, am I doing the 2's ...