(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.
Explanation
(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})
= (3frac{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})