+0 Let x be the binary number (0.001001001 . . .)2 and let y be the octal number (0.666666 . . .)8. What is x + y in decimal?
Please explain your answer.
+410 We can convert these two seperately.
0.001001001... when expressed in Base 2 is 0∗2−1+0∗2−2+1∗2−3+0∗2−4+0∗2−5+1∗2−6...
The terms with the 0's are all 0, so this simplifies into 2−3+2−6+2−9+2−12...
Using the Infinite geometric series formula, (first term)/(1 - common ratio), we get 2−31−2−3which simplifies to 17.
We do the second one similarly, simplifying 0.6666666666666 base 8 into 6∗8−1+6∗8−2+6∗8−3+6∗8−4, using the infinite geometric series formula, we get, 6∗8−11−8−1which simplifies to 67. Adding, 1/7 and 6/7 we get 1.
+410 We can convert these two seperately.
0.001001001... when expressed in Base 2 is 0∗2−1+0∗2−2+1∗2−3+0∗2−4+0∗2−5+1∗2−6...
The terms with the 0's are all 0, so this simplifies into 2−3+2−6+2−9+2−12...
Using the Infinite geometric series formula, (first term)/(1 - common ratio), we get 2−31−2−3which simplifies to 17.
We do the second one similarly, simplifying 0.6666666666666 base 8 into 6∗8−1+6∗8−2+6∗8−3+6∗8−4, using the infinite geometric series formula, we get, 6∗8−11−8−1which simplifies to 67. Adding, 1/7 and 6/7 we get 1.
