# Questions tagged [arithmetic]

Questions about implementing elementary arithmetic operations on a computer with hardware or algorithms. The numbers are often assumed to be in a binary representation, add the [floating-point] tag for arithmetic operations on numbers in a floating point representation.

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### Why is ot returning TRUE in first case and FALSE in the second?

I understand 0.3 does not have an accurate binary representation. Suppose I run the following code: Why is the answer "True" in the first case and "False" in the second? Shouldn't ...
• 101
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### Binary subset rank and unrank

Let there be "N" bits. We want to rank and unrank a specific subset of bit combinations based on the following criteria - ...
• 25
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### Check if sum of positive integers is less than a W integer in CNF

As title says, what I am trying to do is to find a way to sum integers and later compare them with another integer W, in a manner that when the sum of integers is less or equal than W, using only CNF. ...
1 vote
76 views

### smoothness test

An integer is $k$-smooth if its prime factors are at most $k$. In the case where $k$ is not tiny (say $10^8 < k < 10^{10}$), are there algorithms to test for $k$-smoothness, other than trying ...
• 111
1 vote
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### Binary logarithm of binary number using logic gates

I need to use logic gates to calculate the floor of binary logarithm of a binary number $x_{n-1}, ..., x_0$. I know that this can be computed when I find the position of the most significant bit set ...
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1 vote
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### Check if n-bit number is divisible by 7

Show how to check if n-bit number is divisible by 7 in logarithmic circuit depth. How can I construct the circuit to be able to check the divisibility?
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### How does signed floating point adder implement?

The following picture is a block diagram of an arithmetic unit dedicated to IEEE 754 floating-point addition from Computer Organization and Design RISC-V Edition: The Hardware Software Interface 2nd ...
• 109
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### Binary Comparison Between Two Integers

Say I have two integers,i and j, which for the sake of example will be 2 and 5, represented by $010_2$ and $101_2$ respectively. I have a third bit set to 0. If $j \geq i$, then this bit should change ...
249 views

### How do I multiply 2 signed 4 bit numbers in a logic circuit?

I've been experimenting with making a binary calculator lately, and I've got the addition and subtraction working. I now want to start making a multiplier, but I have no idea where to even start. I ...
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1 vote
87 views

### Order in a subset

Lets consider a range of "K" binary digit numbers. In that range, we want to take a subset of those values which have (<="n" consecutive 0s) AND (<="n" consecutive ...
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78 views

### Division of Large Numbers with Known Factors

Consider two large numbers $a$ and $b$ of which some, not necessarily prime factors, are known. This means $a = a_1 \cdot \dots \cdot a_n$ and $b = b_1 \cdot \cdots \cdot b_m$. Required is their ...
41 views

### Exact Definition of simple bit pattern?

I didn't find an exact description for this, but I know that any integer type is a simple bit pattern, it seems to me that the simple bit pattern should have a more exact description as I understand ...
1k views

### Prove HAKMEM Item 23: connection between arithmetic operations and bitwise operations on integers

Prove that for $A, B \in \mathbb{Z}$, $A + B = (A \operatorname{\&} B) + (A \mid B) = (A \oplus B) + 2(A \operatorname{\&} B)$ where $\&$ is bitwise AND, $|$ is bitwise OR and $\oplus$ is ...
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### I need to test the speed of performing arithmetic operations on binary numbers

As part of a college project, I need to compare the speed of arithmetic operations directly in binary on different processors. Example: At what speed will binary addition be performed on an Intel Core ...
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### How can I do a subtraction with a two tape Turing machine

I have already made a Turing machine with just one tape that solves a subtraction between two numbers, but I trying to do the same but with TWO tapes. As an example, how can I solve 4-2? Taking ...
1 vote
2k views

### Represent unsigned 12-bit octal numbers. Results in octal

I have an HW question where I found an answer that matches mine, but their breakdown confuses me. Ques: What is 4365 - 3412 when these values represent unsigned 12-bit octal numbers? The result should ...
• 11
920 views

### Is squaring easier than multiplication? [duplicate]

Let $T_1(n)$ be the time complexity of computing the square of an $n$-bit integer, and let $T_2(n)$ be the time complexity of computing the product of two $n$-bit integers. Assuming that addition is ...
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1 vote
544 views

### Adding two numbers in base 2(floating point) vs Multiplying two numbers in base 2(floating point)

Is it true that adding two numbers in base 2 is more complex than multiplying them? If so can someone please explain why this is the case?
1k views

### How to do -8 x -8 in a 4 bit booth multiplier?

In the general case of an n bit booth multiplier, the maximum negative value is -2n-1. So with 4 bits we can represent -8 x -8 (M=1000, Q=1000). Now if we follow Booth's algorithm for multiplying n-...
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1 vote
169 views

### 2's complement substraction

I need to perform 2's complement operations on -50 - -48 From a mathematical point of view the following would be true. -50 + 48 = -2 If I would follow the steps I would have: I got to this result by ...
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I want to know how switch-efficient a multiplier can be. If I need to do many $N$-bit by $N$-bit multiplies, and each bit is determined by flipping a coin, what's the average number of transistor ...