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Questions tagged [numeral-representations]

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0answers
29 views

Do I need a implicit digit in a base-10 machine?

If I have a base-10 machine, Do I need a implicit bit or all numbers for mantissa take all bits? When I say bits, I mean digits. Since in a base-2 machine, You have a implicit bit. My question is if ...
2
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4answers
68 views

Binary 2s Compliment Applied Twice Gives Original - How?

At the moment the maths behind binary 2s compliment seems like voodoo to me. If I take 0011 (+3) and "flip and add 1", I get 1101 (-3) If I apply the same process to 1101, ("flip and add 1"), I get ...
2
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1answer
103 views

Overflow rule in two's complement arithmetic

In the book by William Stallings the overflow rule overflow rule for 2's complement addition is stated as follows: Overflow rule: If two numbers are added, and they are both positive or both ...
3
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2answers
41 views

Balanced based representation

I'm interested in balanced base $B$ representation for fixed point arithmetic. The paper Fixed-point arithmetic in SHE schemes (Costache, Smart, Vivek and Waller, in Proceedings of 23rd International ...
2
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1answer
40 views

Two's complement general formula

In college, we've seen some general formulas to compute the decimal value a of a binary representation $a_{N-1} \dots a_2 a_1 a_0$ in two's complement, $N$ being the number of bits. For $a \ge 0$ we'...
3
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1answer
44 views

Why does existence of predecessor imply adequacy of a numeral system?

I encountered this result when working with $\lambda$-calculus (so every element I mention here was a $\lambda$-expression there [1]), but I will express everything with, more understandable to ...
4
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2answers
539 views

Which number representation takes the largest amount of memory?

Options are: Signed magnitude One's complement Two's complement Excess notation This is the question from an 'example of a previous exam' I've been given at university. Answers were not provided. ...
1
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1answer
122 views

4-digit 5's complement of a negative number

Let $n = -13, \ k = -24$ How do I find the 4-digit 5's complement of each number? What would be the result of $n + k$ in complement representation? I understand how to calculate $n$-digit, 2's ...
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2answers
1k views

What are the reasons for and against using normalized floating point?

Floating point number formats can be normalized or not, meaning that ‘normal’ floating point numbers have an implicit (hidden) leading bit 1 in the significand. For example, the binary IEEE 754 ...
-1
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2answers
291 views

How many integers can you represent with 6 bits?

I might be wrong but I think it must be 2^6 = 64 integers?
0
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0answers
141 views

Representation of the number in two's complement

We have that MIMA (Neumann MInimal MAchine) has the following commands: I want to write a MIMA program that takes the value $2^{23}-24=8.388.584$ to the memory cell $y$. We have to take ...
55
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12answers
23k views

Does a byte contain 8 bits, or 9?

I read in this assembly programming tutorial that 8 bits are used for data while 1 bit is for parity, which is then used for detecting parity error (caused by hardware fault or electrical disturbance)....
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1answer
591 views

Convert integer of mixed radix to standard positional numeral system and vice versa

I have multiple numbers (e.g. [1, 4, 2]) where each number can be one of a specified range of numbers (e.g. [0-1, 0-5, 0-3]). I ...
0
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1answer
3k views

8-bit floating-point representation

I'm studying about representing fractional numbers as floating-point values. It is going to be an 8-bit representation. Somewhere in the text, it is said that: "We use the first bit to represent ...
1
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2answers
76 views

Why is a negative number a pseudo-positive number in ones' complement?

I'm studying ones' complement representation and I read in a book that a negative number in ones' complement is a pseudo-positive of value $R^n - 1 - |x|$. However there is no demostration and I can'...
12
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5answers
11k views

Will the future quantum computers use the binary, ternary or quaternary numeral system?

Our current computers use bits, so they use the binary numeral system. But I heard that the future quantum computers will use qubits instead of simple bits. Since in the word "qubit" there is the ...
12
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5answers
3k views

Is 2**x faster to compute than exp(x)?

Forgive the naïveté that will be obvious in the way I ask this question as well as the fact that I'm asking it. Mathematicians typically use $\exp$ as it's the simplest/nicest base in ...
1
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1answer
57 views

Can This Property (Representative Property) Be Generalized?

I recently came across with a question that asks for the greatest subset of a given set, which includes relatively prime elements.(Randomly selected item from a set is always relatively prime to all ...
14
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4answers
35k views

Why octal and hexadecimal? Computers use binary and humans decimals

Why do we use other bases which are neither binary (for computers) nor decimals (for humans)? Computers end up representing them in binary, and humans strongly prefer getting their decimal ...
5
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2answers
145 views

Numeral systems other than unary used in nature or in animal and human behaviours

Representing numeric values using positional notation is one of the milestones in the history of arithmetic. Babylons used a base 60 system, Maya a base 20 system; base 10 system became "the standard" ...