0
votes
1answer
45 views

Absolute and relative error of a binary number?

Given is the following system $A:={ \pm 1.a_1 a_2 a_3 a_4 \cdot 2^e}$, $a_{i}\in \left \{ 0,1 \right \}$, $i\in \left \{ 1,2,3,4 \right \}$, $e\in \left \{ -8,\ldots,8 \right \}$. Find the absolute ...
4
votes
1answer
344 views

Finding a rational number which is simply normal to relatively prime bases

Let $n\ge 2\in\mathbb Z$. Suppose that a base-$n$-decimal $(0.a_1a_2a_3\cdots)_n$ represents $\sum_{k=1}^{\infty}\frac{a_k}{n^k}$ where $a_{i}\in\{0,1,\cdots,n-1\}\ (i=1,2,\cdots)$ is each digit ...
0
votes
3answers
195 views

How do I add multiple binary numbers without using a partial sum?

I know how to add binary numbers but what I normally do is add the first 2 binary numbers and then add the 3rd one to their sum. It is really slow. $$ 111_2 + 111_2 + 111_2 + 111_2 $$ Here is ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 = ...
1
vote
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) ...
3
votes
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, ...
0
votes
1answer
167 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: ...
1
vote
2answers
157 views

Binary to Decimal

Is it possible to convert a binary pattern to decimal pattern consists of 0's and 1's without loop (iterations). Suppose if I have. ...
0
votes
0answers
50 views

Binary String as number

For 1 ≤ i ≤ n− m, m < n, Interpreting the strings as binary numbers, we have that A[(i+ 1) ..(i+ m)] = 2 A[i..(i+ m− 1)] − (2^m−1)A[i]+ A[i+ m]. Can someone ...
15
votes
8answers
3k views

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?
3
votes
4answers
4k views

binary representation of a real number

In Baby Rudin,I find reference to the fact that the binary representation of a real number implies the uncountablity of the set of real numbers.(page 30)But I have two questions: Does every real ...
1
vote
2answers
582 views

Where does binary arithmetic/manipulation enter the mathematics/engineering curriculum?

Binary arithmetic is both an educational basis for elementary logic and an pervasive tool for practical mechanics in managing computer systems (at a very particular level). That is the state of ...