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43 views

Newbie: hexadecimal editors to make sense of binary files

As a disclaimer, I am a geophysicist, not a computer scientist. I have a binary file with a whole bunch of data in it (it is a large file; 221 MB). I am trying to convert this to something usable but ...
59 views

Long multiplication school method: number of primitive operations to calculate first partial product?

Having got some basics down in regard to addition and explaining it in terms of primitive operations (addition and multiplication), I am now again stuck on understanding the more complicated long ...
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Difference between cordic algorithm and table based methods for elementary functions computation

In this book both Table Based methods and Cordic iterations are explained. computationally speaking i suppose the Table based is usually faster, even though it probably requires more resource, while ...
15 views

Implementing 16bit Adder from 4bit CLAs

It's a bit confusing to me how this 16bit CLA adders work. Since it is hard to implement 16 bit CLA logics and circuits directly, we cascade 4bit CLAs in two's multiples to achieve this. So the ...
312 views

Does a shift operation distribute over XOR

In this question, we abuse the mathematical notation to express bitwise operations in the following way: $\ll$ is a binary left shift $\oplus$ is a bitwise XOR $0b1, 0b110, 0b10 \ldots$ are used to ...
46 views

Generally, does the time it takes to compute (n mod m) depend on the size of n?

Example: Suppose I have a number a with 100 decimal digits, b with 200 decimal digits, and m with 10 decimal digits. Would the speed of the computation a mod m vary greatly from b mod m because of ...
36 views

Using SMT Solvers in formula checking

I'm currently working on a static analysis work in which I need to check whether a given formula is met or not. I hope the following example clarifies my requirement. Suppose we have a list of three-...
74 views

Complexity of division

The article Computational complexity of mathematical operations mentions that the complexity of division in $O(M(n))$, and that "$M(n)$ below stands in for the complexity of the chosen multiplication ...
36 views

How fast can one compute the power of a number?

Let $x \in \mathbb{R}$ and $k \in \mathbb{Z}^+ \cup \{0\}$ then how fast can one compute $x^k$? If $x, k \in \mathbb{Z}$ then I guess this previous discussion already settled that, How many ...
23 views

Dual Signed Kahan Summation

NOTE: This is for a project I'm working on for fun, NOT production code. So I'm working on a pet project that involves reading data in from a sensor and summing it up. The values are mostly ...
25 views

half precision floating point multiplication

A = 0 10011 0011110111 B = 1 00011 0010011000 exponent is 15, mantissa is 10 bits and first bit is implicit. Can somebody please tell me the final answer cause I am having trouble figuring ...
37 views

Why do floating point additions sometimes produce equal results? [duplicate]

I have tried two sentences on my computer : 2 + 10^(-18) == 2 2^(-55) + 2^(-57) == 2^(-55) My computer gives TRUE and FALSE respectively. Why does the computer ...
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How would you recursively add numbers? Just in terms of pseudocode how would one approach such a problem in the most efficient run time
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Is the number of operators always one less than the number of values in an arithmetic Reverse Polish Notation expression with only binary operators?

Is the number of operators always one less than the number of values in an arithmetic Reverse Polish Notation expression with only binary operators? This question seems very trivial, but I don't know ...
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Help me understand the logic behind x - y in binary by boolean?

x and y are 4 bit signed numbers (2s complement..) x - y can be obtained by: !(!x + y) I know that in 2s complement ...
104 views

XOR two numbers

Is there an intuitive meaning of XOR of two numbers not involving binary and just decimal? Or is is always converted into binary and then XORed?
310 views

Minimal basis for set of binary vectors using XOR

I would be surprised if this isn't a well-studied problem, but I'm not sure what else to search for at this point: you're given a set of binary $n$-vectors $S \subset \{0,1\}^n$. The problem is to ...
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Is it possible to compute -12 (decimal) in 4 bits binary

This is what I have so far 1 1 0 0 Switch values by 2s Complement 0 0 1 1 + 1 0 1 0 0
546 views

Complexity of multiplication

I've been reading around the area of complexity and arithmetic operations using logic gates; one thing that is confusing me is that $$\Theta (n^{2})$$ is quoted as being ...
67 views

What is the XNOR of 3 or more inputs?

We know that for 3 variables (A=0,B=1,C=1), f$_1$ = (A XNOR B XNOR C) = 1, since the input has even number of 1's. But if we were to do this step by step, f$_2$ = (A XNOR (B XNOR C)) = (A XNOR (1 ...
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This opertion gives overflow and carry?

Take this example in 2's complement representation with 8 bits. 1111 1110 + 1111 1110 ( -2 + -2 = -4 ) Calculation: ...
2k views

I'm having some trouble figuring out where the "Carry in" value comes from in respects to a one bit full adder diagram. I understand the below half adder, but my question is: is the the output of ...
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276 views

Calculating the number of multiplications necessary to evaluate a polynomial

I was watching a lecture and got confused over a slide. This is what it says: Consider a polynomial - first representation $$P = 2 + 4x^{3} + 8x^{6} + 7x^{25} + 6x^{99}$$ The ...
293 views

Algorithm for multiplying multivariate polynomials

Let $R$ be a commutative ring. Let $f(x_1, \dots, x_n), g(x_1, \dots, x_n)$ be two multidimensional polynomials in $R$ with maximal total degree $\delta$. How fast can we compute the product of $f$ ...
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pragmatic way to compute/ search/ match MSBs operation

consider integers represented as base 2 (strings). define a relation called "n-msb matching" that is true when the 1st n msbs (MSB is "most significant bits") match (of two integers). what is a ...
275 views

How was the ALU implemented in the first computer (i.e., Babbage's analytical engine)?

I've seen circuit level implementations of ALU's before, but how are NOT/AND/ADD performed mechanically?