Which one of the following equations is true? A. (11)_2+(100)_2=(1011)_2B. (1100)_2/(11)_2=(11)_2C. (10)_2+(1011)_2=(1110)_2D. (10000)_2−(100)_2=(1100)_2
Question
Which one of the following equations is true?
A. (11)_2 + (100)_2 = (1011)_2
B. (1100)_2 / (11)_2 = (11)_2
C. (10)_2 + (1011)_2 = (1110)_2
D. (10000)_2 − (100)_2 = (1100)_2
Solution
Sure, let's go through each equation one by one:
A. (11)_2 + (100)_2 = (1011)_2 Converting each binary number to decimal, we get: (3)_10 + (4)_10 = (11)_10 This is not true, so A is not the correct equation.
B. (1100)_2 / (11)_2 = (11)_2 Converting each binary number to decimal, we get: (12)_10 / (3)_10 = (3)_10 This is not true, so B is not the correct equation.
C. (10)_2 + (1011)_2 = (1110)_2 Converting each binary number to decimal, we get: (2)_10 + (11)_10 = (14)_10 This is true, so C is the correct equation.
D. (10000)_2 - (100)_2 = (1100)_2 Converting each binary number to decimal, we get: (16)_10 - (4)_10 = (12)_10 This is not true, so D is not the correct equation.
So, the correct equation is C. (10)_2 + (1011)_2 = (1110)_2.
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