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3 years ago

Convert A4B from hexadecimal to binary. Show your work.

Computers and Technology

1 answer:

Rama09 [41]3 years ago

3 0

Answer:

The answer is A4B₁₆ = 2635₁₀ = 101001001011₂

Explanation:

To convert from hexadecimal base system to binary base system, first you can do an intermediate conversion from hexadecimal to decimal using this formula:

where position of the x₁ is the rightmost digit of the number and the equivalents hexadecimal numbers to decimal:

A = 10.
B = 11.
C = 12.
D = 13.
E = 14.
F = 15.

A4B₁₆ = A*16²+4*16¹+B*16⁰ = 2560 + 64 + 11 = 2635₁₀

Now, you have the number transformed from hexadecimal to decimal. To convert the decimal number 2635 to binary: Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to 0:

2635 ÷ 2 = 1317 + 1;

1317 ÷ 2 = 658 + 1;

658 ÷ 2 = 329 + 0;

329 ÷ 2 = 164 + 1;

164 ÷ 2 = 82 + 0;

82 ÷ 2 = 41 + 0;

41 ÷ 2 = 20 + 1;

20 ÷ 2 = 10 + 0;

10 ÷ 2 = 5 + 0;

5 ÷ 2 = 2 + 1;

2 ÷ 2 = 1 + 0;

1 ÷ 2 = 0 + 1;

Now, construct the integer part base 2 representation, by taking the remainders starting from the bottom of the list:

2635₁₀ = 101001001011₂

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#include <iomanip>

#include <iostream>

#include <math.h>

using namespace std;

// C++ program to illustrate

// how to calculate BMI

float BMI(float height, float weight)

{

float bmi = weight / pow(height, 2);

return bmi;

}

int main()

{

float height = 1.79832;

float weight = 70;

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float bmi = BMI(height, weight);

cout << "The BMI is " << setprecision(15) << bmi

<< " so ";

// Conditions to find out BMI category

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cout << "underweight";

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cout << "Healthy";

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cout << "overweight";

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return 0;

}

// This code is contributed by aarohirai2616.

<h3>Output: </h3>

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