Given an 10-bit two's complement binary number, what is the decimal value of the largest negative integer that can be represente
1 answer:
<h2>Answer:</h2><h2></h2>
The largest negative integer is -512
<h2>Explanation:</h2><h2></h2>Method One
<em>=>Unsigned binary numbers</em>
In a regular representation of unsigned integers, using n bits, the total number of numbers that can be represented is . But since zero will be included, the range of numbers that can be represented is from 0 to
- 1.
For example, using 4 bits, numbers from 0 to - 1 can be represented i.e numbers from 0 to 15.
Given a 5-bit, the number will range from 0 to - 1 which is 0 to 31.
<em>=> Signed binary numbers.</em>
In a signed number representation (e.g 2's complements), using n bits, the total number of numbers that can be represented is still . But since the signs of the number matter (positive and negative integers), the range of numbers that can be represented is from
to 0 to
- 1.
For example, using 4 bits, numbers from
=> - to 0 to
- 1.
=> - to 0 to
- 1.
=> -8 to 0 to 7.
That means that for a 4-bit representation;
the largest positive integer is 7 and
the largest negative integer is -8
Using this logic, for a 10-bit 2's complement number, the numbers will range from
=> - to 0 to
- 1.
=> - to 0 to
- 1.
=> -512 to 0 to 511
That means that the
largest positive integer is 511
largest negative integer is <em>-512</em>
Method Two
Given an hypothetical 10-bit two's complement binary number as follows:
x x x x x x x x x x
In 2's complement representation, when the most significant bit is 1, the number is negative and if 0 it is positive.
<em>Note </em><em>: </em><em>The most significant bit (MSB) of a binary number is the leftmost digit. For example, 1000 has an MSB of 1 and 0111 has an MSB of 0.</em>
Since we want to get the largest negative integer, then the MSB of the 10-bit 2's complement binary number written above should be 1.
=> 1 x x x x x x x x x
The MSB has been represented, then the remaining 9 bits are the value of the number to be represented. To get these, please note that the largest negative integer will have the smallest value. The smallest value attainable is therefore 000000000.
Combining the MSB(1) and the smallest value(000000000) gives
=> 1000000000
Note: This (1000000000) is the 2's complement representation of the largest negative integer. To convert it to decimal,
(a) first we flip all its bits and add 1 to the result as follows:
=> 0111111111 + 1
=> 1000000000
(b) then do the conversion to decimal as follows:
1000000000 = 1 x + 0 x
+ 0 x
+ 0 x
+ 0 x
+ 0 x
+ 0 x
+ 0 x
+ 0 x
+ + 0 x
= 512
Therefore, 1000000000 is -512 in decimal and it is the largest negative integer representable.
<em>Hope this helps!</em>
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Answer:
Following is given the solution to each part.
All the comments are given above each step so that they can make the logic clear.
I hope it will help you!
Explanation:
Answer:
Here is the C++ program:
#include <iostream> //to use input output functions
using namespace std; //to identify objects cin cout
int main() { //start of main method
int red,green,blue,smallest; //declare variables to store integer values of red,green, blue and to store the smallest value
cout<<"Enter value for red: "; //prompts user to enter value for red
cin>>red; //reads value for red from user
cout<<"Enter value for green: "; //prompts user to enter value for green
cin>>green; //reads value for green from user
cout<<"Enter value for blue: "; //prompts user to enter value for blue
cin>>blue; //reads value for blue from user
//computes the smallest value
if(red<green && red<blue) //if red value is less than green and blue values
smallest=red; //red is the smallest so assign value of red to smallest
else if(green<blue) //if green value is less than blue value
smallest=green; //green is the smallest so assign value of green to smallest
else //this means blue is the smallest
smallest=blue; //assign value of blue to smallest
//removes gray part by subtracting smallest from rgb
red=red-smallest; //subtract smallest from red
green=green-smallest; //subtract smallest from green
blue=blue-smallest; //subtract smallest from blue
cout<<"red after removing gray part: "<<red<<endl; //displays amount of red after removing gray
cout<<"green after removing gray part: "<<green<<endl; //displays amount of green after removing gray
cout<<"blue after removing gray part: "<<blue<<endl; } //displays amount of blue after removing gray
Explanation:
I will explain the program using an example.
Lets say user enter 130 as value for red, 50 for green and 130 for blue. So
red = 130
green = 50
blue = 130
First if condition if(red<green && red<blue) checks if value of red is less than green and blue. Since red=130 so this condition evaluate to false and the program moves to the else if part else if(green<blue) which checks if green is less than blue. This condition evaluates to true as green=50 and blue = 130 so green is less than blue. Hence the body of this else if executes which has the statement: smallest=green; so the smallest it set to green value.
smallest = 50
Now the statement: red=red-smallest; becomes:
red = 130 - 50
red = 80
the statement: green=green-smallest; becomes:
green = 50 - 50
green = 0
the statement: blue=blue-smallest; becomes:
blue = 130 - 50
blue = 80
So the output of the entire program is:
red after removing gray part: 80 green after removing gray part: 0 blue after removing gray part: 80
The screenshot of the program along with its output is attached.
