# Tagged Questions

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

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### Fractions in binary?

How would you write a fraction in binary numbers; for example, $1/4$, which is $.25$? I know how to write binary of whole numbers such as 6, being $110$, but how would one write fractions?
733 views

### Algorithm for creating binary rational numbers

I read here an algorithm to convert a decimal rational number to binary by multiplications by 2, but although it's very simple to carry on, I still haven't managed to explain myself why it works. ...
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### Finding Expressively Adequate truth Functions

I was wondering if someone could help me count the total number of Truth Functions of 3 variables, that can generate all the possible truth functions.. I got 56 but I'm not sure of the answer. EDIT: ...
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### The sum of powers of two and two's complement – is there a deeper meaning behind this?

Probably everyone has once come across the following "theorem" with corresponding "proof": $$\sum_{n=0}^\infty 2^n = -1$$ Proof: $\sum_{n=0}^\infty q^n = 1/(1-q)$. Insert $q=2$ to get the result. Of ...
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### 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.
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### 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
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### Function that sends $1,2,3,4$ to $0,1,1,0$ respectively

I already got tired trying to think of a function $f:\{1,2,3,4\}\rightarrow \{0,1,1,0\}$ in other words: $$f(1)=0\\f(2)=1\\f(3)=1\\f(4)=0$$ Don't suggest division in integers; it will not pass for ...
3k views

### How do you work with the IEEE 754 32-bit floating point format?

I'm having trouble completing a question that deals with the IEEE 754 32-bit floating point format, primarily because I don't know how to use it. I was hoping someone here could clarify for me using ...
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### Recursively defining sets of strings discrete math

So here are the two problems: Recursively define the set of bit strings K that do not have 00 as its substring. How many bit strings of length 10 are included in the above set K? Can someone ...
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### How many numbers from $1$ to $2^n$ will have $11"$ as substring in binary representation?

For example say, $n = 2$. So our set is $\{1, 2, 3, 4\}$ in base $10$ and $\{1, 10, 11, 100\}$ in base $2$. So Output $1$, because only one number i.e. $3$ is there such that it has $11"$ in it. ...
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### An odd question about induction.

Given $n$ $0$'s and $n$ $1$'s distributed in any manner whatsoever around a circle, show, using induction on $n$, that it is possible to start at some number and proceed clockwise around the circle to ...
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### 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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### Binary long division for polynomials in CRC computation

I am trying to learn binary long division, and I am confused. An example in my book gives that $10011010000/1101 = 11111001$ plus a remainder of $101$, which doesn't make sense, since $1001$ is not ...
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### How would I take multiple single bit binary numbers and convert it into a single binary array number?

So lets say I have these: 101010101001 Now lets also say I didn't count them you should count binary, lets say I counted that number at 6 because their are 6 1s and the 0s don't count. Now how would ...