# Questions tagged [numeral-representations]

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4answers
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### Is there a binary representation where the encoding distance grows with the arithmetic distance?

I need to binarily encode/decode small integers (around 10 bits), in such a way that the hamming distance of the encoded number grows monotonically with the (absolute value) arithmetic distance of the ...
1answer
131 views

### Unsigned/signed boolean

Answer is c). I understand that the expression evaluates to true but what does signed/unsigned have to do with booleans?
0answers
28 views

### Efficient parameterization of low vertex count polygons

I'm trying to design a method to represent polygons as vectors. There are many ways to do this, but I have a few goals and I'm not sure what representation is best to fulfil these. The objectives are: ...
2answers
191 views

### Streaming digit-to-digit conversion from decimal to hexadecimal

I am looking for a streaming algorithm for converting a decimal number to a hexadecimal number. I am assuming the input is a string represention of a decimal number (i.e., each character is a decimal ...
1answer
206 views

### Normalization in IBM hexadecimal floating point

According to the Wikipedia link of IBM hexadecimal floating point: Consider encoding the value −118.625 as an IBM single-precision floating-point value. The value is negative, so the sign ...
1answer
35 views

### Conversion from octal numerical system to binary numerical system

I know that in order to convert a numeral in base-8 to a numeral in base-2 I can write each octal digit as a binary word of 3 bits. I know that 2^3 = 8 that is exactly the dimension of the base of ...
2answers
118 views

### 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, ...
4answers
775 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 ...
1answer
4k 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 ...
2answers
45 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 ...
1answer
149 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'...
1answer
46 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 ), but I will express everything with, more understandable to ...
2answers
758 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. As ...
2answers
763 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 ...
2answers
3k 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 ...
2answers
1k views

### How many integers can you represent with 6 bits?

I might be wrong but I think it must be 2^6 = 64 integers?
0answers
152 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 ...
12answers
26k 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)....
1answer
910 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 ...
1answer
6k 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 ...
2answers
117 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'...
5answers
17k 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 ...
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 ...
1answer
58 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 ...
5answers
42k 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 ...
2answers
160 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" ...