1
vote
2answers
108 views

Why 5.8 (decimal) is 101.11001100… (binary)?

I would like to know why 5.8, in decimal 101.11001100..., in binary, a recurring decimal?
0
votes
2answers
49 views

Convert HEX to BIN

How to convert the number $fada.cafe_{16}$ to binary? I used Wolfram understand it, but when I type $fada.cafe_{16}$, it changes to $fada.cafdfffffd..._{16}$. Why that?
1
vote
2answers
53 views

Help with natural number problems

Suppose that $\mathbb{F}$ is an ordered field with identities $0$ and $1^{\star}$ (in this problem, $1 \in \mathbb{N}$ ) Define inductively $f: \mathbb{N} \rightarrow \mathbb{F}$ by: $$f(1) = ...
-1
votes
3answers
126 views

Converting Base 16 digits to base 2 and 10 - Analysis Question

With base $16$, the digits are denoted as $0, 1,\ldots, 9, A,\ldots, F$. Let $n = AB_3$. Rewrite $n$ with bases $10$, $2$. I have no clue what this question means and how I should attempt to do this. ...
0
votes
1answer
126 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: ...
2
votes
3answers
73 views

In a numerical system of base $r$, the polynomial $x^2 − 11x + 22 = 0$ has the solutions $3$ and $6$. What is the base r of the system?

From Algebra, the statement is equivalent to say that $(x^2− 11x + 22)_{r}$ = $(x − 3)_{r} \cdot (x − 6)_{r}$. Doing operations we arrive at $3 + 6 = 11_{r} = r + 1$, and $(3)(6) = 22_{r} = 2 \cdot ...
2
votes
1answer
92 views

Is notation of a number in base-(-2) numeral system unambiguous?

I have a problem with proving this thesis: Notation of a number in base-(-2) numeral system is unambiguous. I think I need to use mathematical induction, but I don't know how.
0
votes
2answers
55 views

How can I demonstrate that the decimal equivalent for a binary number consisting of $n$ $1$'s is $2^n-1$?

I know that $2^n-1$ gives you the decimal equivalent for any word consisting of $n$ $1$'s, but how can I demonstrate that in general terms for any word of $n$ $1$'s?
1
vote
3answers
97 views

Mathematical Systems Question Help

Alright, this is another question for my math for teachers course. This question is not actually in the homework, but there are problems similar to it. I'd really like to learn how to do problems like ...
0
votes
1answer
69 views

Is Multiplication A System?

I don't understand how to identify the properties of a system. What possible properties could a system have? Are a certain number of properties required in order to be classified as a system? The ...
1
vote
1answer
113 views

Numerology and the possible combinations

I was looking into numerology and it's pretty interesting to see how your name and birthdate are broken down into numbers and the categories that are used to assign numbers to them. My breakdown is ...
1
vote
2answers
71 views

Base 2 for 2010

To express 2010 in base 2, we use exactly 8 ones and 3 zeros. Find the next two integers in base 2 that use the same number of ones and zeros.
2
votes
2answers
62 views

DUODEC to BIN, OCT, DEC problem

I am a new student of basic Mathematics and I am learning number systems, so this is a basic question. This exercise gives me the following duodecimal number: 9AX (where A=11, X=10) And it requires ...
0
votes
1answer
440 views

Representation of Number in hexal system

A number written as 213 in quadral system (number system with base 4) will be represented in hexal system (number system with base 6) as (A) 23 (B) 39 (C) 103 (D) 303
0
votes
1answer
2k views

Single precision numbers and double precision numbers

I just came across this in my work and find it rather baffling: ...
0
votes
1answer
88 views

Exponent e of 5 bits alias 16

I was reading my notes and came across the following ...
0
votes
1answer
3k views

Converting decimal number to a hexadecimal number

I'm trying to represent the number 12.25 in various bases. So without normalizing: For Binary: ...
2
votes
2answers
581 views

How many even numbers between 10,000 and 20,000 have distinct digits?

This is a combinatorics problem I must solve: How many even numbers between 10,000 and 20,000 have distinct digits(i.e no repetitions)? Is the way I solved it correct? I put for lines for ...
2
votes
1answer
354 views

convert fractions from one base to another using repeated multiplications

I have to convert a number that looks like this 254.3212 base 6 to base 3. Now I can manage the decimal part (254) but I'm having trouble with the fraction (3212). How do I convert the fractional part ...
1
vote
4answers
3k views

Convert numbers from one base to another using repeated divisions.

I have a homework assignment for my programming class to implement an algorithm that can convert from bases 2 trough 16 to any other base from 2 trough 16 but with a few twists. What I need to ...
1
vote
1answer
69 views

Problem in converting from hex to dec

I understand that unsigned representation does not have negative numbers but I am stuck with a question, I have to convert B which is a ...
2
votes
2answers
538 views

Stuck with IEEE-754 format (binary to decimal conversion)

I am stuck with a problem, Now here is the formula applied to a question, The red colored bits show the exponent(e) while, the yellow bits are fraction (f). Now I am confused with how did the ...
1
vote
2answers
6k views

Conversion from binary fraction to octal

Can someone verify my results? Binary to Octal 1) 10101.11 is 25.75 2) 0.01101 is 0.6875 3) 10110110.001 is 266.125
1
vote
1answer
128 views

bases and binary

I can not figure this out. I started off by making a table and putting the base(2) on one side, the number in the middle and the remainder in the third row and for 2010 I got 11111011010 but I cant ...