Answer:
1×2-1 = 1/(21) = 1/2 = 0.5
1×2-1 = 1/(21) = 1/2 = 0.5
Recall
that X-n means 1/Xn.
So, 2-2 = 1/4 and
2-3 = 1/8.
To convert an expression in base two notation to base ten notation,
just do the arithmetic.
Here is 100.101 convered from binary representation to decimal representation:
| 1 | 0 | 0 | . | 1 | 0 | 1 |
| 1×22 | 0×21 | 0×20 | . | 1×2-1 | 0×2-2 | 1×2-3 |
| 1×4 + | 0×2 + | 0×1+ | . | 1×0.5 + | 0×0.25 + | 1×0.125 |
| 4 + | 0 + | 0 + | . | 0.5 + | 0 + | 0.125 |
| 4 | . | 625 |
As you work, keep track of what parts of the expression are in base two and what parts are in base ten. In the above, the first row is in base two, the bottom row is in base ten, and the middle rows are polynomials.