Answer to Question #119199 in Combinatorics | Number Theory for Evelyn Teye

Question #119199
Compute the sum of all the numbers represented by a 4-bit unsigned binary number.
1
Expert's answer
2020-06-01T18:08:28-0400

We know that 4-bit unsigned integers range from 0000 to 1111 in binary numeral system (see http://www.cs.uwm.edu/classes/cs315/Bacon/Lecture/HTML/ch04s10.html).

"0000_2 = 0_{10}, \\;\\; 1111_2= (2^3+2^2+2^1+2^0)_{10} = 15_{10}."

Therefore, there are 16 numbers from 0 to 15.

We know that the sum of numbers from 1 to n can be calculated as "\\dfrac{n(n+1)}{2}" (see https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF). So the sum of integers from 0 to 15 will be

"0 + \\dfrac{15\\cdot16}{2} = 120"


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Comments

Assignment Expert
02.06.20, 21:46

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EVELYN
02.06.20, 13:00

thanks

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