(a) Copy and complete the binary multiplication table:
| x | 10 | 11 | 100 | 101 |
| 10 | 100 | 1000 | ||
| 11 | 110 | 1100 | ||
| 100 | 10000 | 10100 |
(b) Convert \(11.011_{two}\) to a number in base ten.
(c) Simplify \(\frac{9.6 \times 10^{18}}{0.24 \times 10^{5}}\) and express your answer in the form \(P \times 10^{m}\) where 1 < P < 10 and m is an integer.
(a)
| x | 10 | 11 | 100 | 101 |
| 10 | 100 | 110 | 1000 | 1010 |
| 11 | 110 | 1001 | 1100 | 1111 |
| 100 | 1000 | 1100 | 10000 | 10100 |
(b) \(11.011_{two} = 1 \times 2^{1} + 1 \times 2^{0} + 0 \times 2^{-1} + 1 \times 2^{-2} + 1 \times 2^{-3}\)
= \(2 + 1 + 0 + \frac{1}{4} + \frac{1}{8}\)
= \(3\frac{3}{8}\)
= \(3.375\)
(c) \(\frac{9.6 \times 10^{18}}{0.24 \times 10^{5}} \equiv \frac{9.6 \times 10^{18}}{2.4 \times 10^{4}}\)
= \(\frac{9.6}{2.4} \times 10^{18 - 4}\)
= \(4 \times 10^{14}\)
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