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Questions tagged [numeral-representations]

32 questions
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votes
12 answers

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). Is this true?
xtt
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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 representation. Why not stick to these two bases?
Quora Feans
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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 word "bi" I first thought that this meant that…
Core-Crash
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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 theory (due to calculus). But computers seem to do everything in…
isomorphismes
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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" used by modern civilizations; digital computers…
Vor
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4
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2 answers

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. As far as I understand only one answer must be…
Evgenia Karunus
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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 back to the original positive value. How is this…
Robin Andrews
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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 negative, then overflow occurs if and only if the result…
RajS
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3
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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 broader audience, notions of…
Sandro Lovnički
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How much can we trust mathematical software when working with large numbers, and how much memory it needs to work with these numbers?

For example, I want to evaluate the expression: $3^{3^{{3}^{3}}}$ so I used wolframalpha.com (it's free, and I don't own any software), which returned the scientific notation of the number above, namely: $ 1.258014290627491317860390698... ×…
Pinteco
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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 Conference on Selected Areas in Cryptography (SAC…
dfine
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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've seen $a= \sum_{i=0}^{N-2} a_i 2^i$, which seems…
L3k
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2 answers

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 complement. I convert it to base 2, invert and add…
yarafoudah
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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 think one can represent my so chosen numbers by seeing them as digits of a number in the mixed radix numeral system with…
mxscho
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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 the sign (1 for negative, 0 for positive), the…
Dsaki
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