(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 b...
Question 1 Report
(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.
Answer Details
(a) Binary multiplication table. Multiply in base ten, then convert back to base two (e.g. \(11\times 11 = 3\times 3 = 9 = 1001_{two}\), \(11\times 101 = 3\times 5 = 15 = 1111_{two}\)).
| \(\times\) | 10 | 11 | 100 | 101 |
|---|---|---|---|---|
| 10 | 100 | 110 | 1000 | 1010 |
| 11 | 110 | 1001 | 1100 | 1111 |
| 100 | 1000 | 1100 | 10000 | 10100 |
(b) Convert \(11.011_{two}\) to base ten.
\[1\times 2 + 1\times 1 + 0\times\tfrac{1}{2} + 1\times\tfrac{1}{4} + 1\times\tfrac{1}{8} = 2 + 1 + 0.25 + 0.125 = \mathbf{3.375}\](c) Simplify.
\[\frac{9.6\times 10^{18}}{0.24\times 10^{5}} = \frac{9.6}{0.24}\times 10^{18-5} = 40\times 10^{13} = 4.0\times 10^{14}\]So \(P = 4.0\) and \(m = 14\).
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