(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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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) \(\frac{9.6 \times 10^{18}}{0.24 \times 10^{5}} \equiv \frac{9.6 \times 10^{18}}{2.4 \times 10^{4}}\)
= \(\frac{9.6}{2.4} \times 10^{18 - 4}\)
= \(4 \times 10^{14}\)
Source: Myschool Past Questions Archive (Record #54467)