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Mathematics
JAMB
The equivalent of (10110.011)
2
in base 10 is?
A.
26.325
B.
24.372
C.
42.443
D.
22.375
Correct Answer:
22.375
Explanation
Using the expansion method on (10110.011)
2
(1 * 2
4
) + (0 * 2
3
) + (1 * 2
2
) + (1 * 2
1
) (0 * 2
0
) + (0 * 2
-1
) + (1 * 2
-2
) + (1 2
-3
) (1*16) + 0 (1*4) + (1*2) + 0 + 0 + (1*1/4) + (1*1/8) 16 + 4 + 2 + (0.25 + 0.125) 22 + 0.375 (10110.011)
2
= 22.375
10
Using the expansion method on (10110.011)
2
(1 * 2
4
) + (0 * 2
3
) + (1 * 2
2
) + (1 * 2
1
) (0 * 2
0
) + (0 * 2
-1
) + (1 * 2
-2
) + (1 2
-3
) (1*16) + 0 (1*4) + (1*2) + 0 + 0 + (1*1/4) + (1*1/8) 16 + 4 + 2 + (0.25 + 0.125) 22 + 0.375 (10110.011)
2
= 22.375
10
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