# Tagged Questions

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

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### What is the best function to increment a cycling counter over a finite (binary) integer representation?

What is the best function to increment a cycling counter over a finite (binary) integer representation? Edit 1 : i found this https://en.wikipedia.org/wiki/Ring_counter#Johnson_counter Edit 2 : ...
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### Are all binary sequences that terminate with $0$s countable?

Consider a subset of binary sequences that contains all binary sequences that terminate with a $0$. For example, $001000...$ and $111100000...$. Is this set countable? I think it is not because the ...
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### Fraction of length-$n$ binary numbers satisfying a constraint

Problem: Derive an expression for the fraction of length-$n$ binary numbers that do not contain the subsequence $010$. Background: The total number of $n$-bit binary numbers is of course $2^n$. ...
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### Exhaustive path through 2^n bit configurations

There's a little play by Samuel Beckett called 'Quad' that consists of nothing else than 4 characters walking on and off stage, one at a time. No two actors leave/enter simultaneously, so only one ...
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### Why Do we reverse the order of digits to get binary number from decimal number [closed]

I know how we get binary numbers from decimal using repeats of division until quotients is 1.But i want to know more on why do we reverse the order of digits to get binary number from decimal number? ...
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### Why are binary numbers ordered the way they are? [duplicate]

Counting to 7 in binary looks like this: 0 1 10 11 100 101 110 111 The highest value is always to the left. But would it make more sense to to it like this? Is there a way that this was picked, or ...
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### Does this rule eventually lead to $0^n1^n$

If you're given a binary string of the form $a_1a_2\ldots a_n \overline {a_1a_2\ldots a_n}$, will the following rule applied a finite number eventually lead to the string $0^n1^n$ where exponentiation ...
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### How to subtract fractional numbers using complements.

I know how $10$'s and $9$'s complements are used, but I don't know how to use complements to subtract two fractional numbers. For example $108.32-26.30$ . How will we solve it using $10$'s and $9$'s ...
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### Write negative decimal in binary(octal etc..) by hand

How do I convert a negative decimal number into other systems(binary, octal)? I got the decimal numbers: -22,5 , -60 and 166. I have to convert them to binary(16 bit) and octal(by hand). I know the ...
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### convert Hex value to two's Complement

for example, let's say: 0xE5 assume the system is 8 -bit in decimal it's = 229 and in Binary it's = 1110 0101 the Two's Complement rules said: sign-bit, which's the most left, indicates a negative ...
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### Binary to Gray code using XOR boolean expressions

I have a question which asks to design a circuit to convert from binary to gray code, using a boolean expression. Now I understand you have to use XOR to achieve this. And I understand that XOR ...
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### Binary arithmetic - overflow and carryout at same time?

In binary arithmetic, When you subtract 2 signed numbers you must discard the carry out. My question is, is it possible for overflow to occur and a carry out? So, on paper there would be two extra ...
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### Convert hexadecimal to binary scientific notation using IEEE 754 single-precision floating point

I am trying to convert these numbers to binary scientific notation, but I cannot figure out the process. Could someone please the process of going about solving this? For IEEE 754 single precision ...
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### What points in $[0,1)$ will have two binary expansions?

What points in $[0,1)$ will have two binary expansions? I know that $\frac{1}{2}$ has the two expansions $0.1\bar{0}$ and $0.0\bar{1}$ $0.1\bar{0}$ is found by starting with $\frac{1}{2}$ and ...
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### Probability of Binary Word Matching

Thanks for reading. Would be lovely if somebody could help me out on this (but not just post the answer) but also how you got there. I'm a programmer and I've ran across this problem which I can't ...
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### Name of this formula or more explantation of the proof?

I have found this formula which is a combinatorial identity for counting binary words. I'd like more information on it, or the name of the proof. I am also not totally clear on the step between the ...
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### Floating point binary to half precision floating point

I am trying to convert to $16$ bit half precision floating point however I ran into a possible error and am unsure if a negative exponent is ok. I am trying to convert $0010011100010000$ I separate ...
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### Show that every number $a$ can be shown in the following form: $a=\sum_{i=1}^{k}2^{x_i}\cdot 3^{y_i}$

Show that every integer $a>0$ can be shown in the form: $$a=\sum_{i=1}^{k}2^{x_i}\cdot 3^{y_i}$$ where $0\le x_1< x_2< \dots < x_k$ and $0\le y_k < y_{k-1} < \dots < y_1$ are ...
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### With 8 bits is it possible to obtain an integer in more than one way? [duplicate]

This is just a curiosity that just came to my mind while thinking at IP addresses. A byte is composed of 8 bits. A bit can either be $0$ or $1$. IPv4 addresses are composed of a group of 4 bytes. ...
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### why $10$ in any base number system written as $10?$

I am a student trying to write an article in number system can same one give me an idea why $10$ in any base number system written as $10$ $?$
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### Binary to Decimal Right of The Binary Point

I need to convert 10000000110.011 to decimal. The first part I fully understand, 2^10 + 2^2 + 2^1 = 1030. Wolfram Alpha confirmed that 1030 is correct. But for the right of the binary point, WA gives ...