Question

2. Convert the following binary numbers into decimal numbers.
a.
101110
b. 101010
c. 111001
d. 000101​

Answer 1

Step-by-step explanation:

$a):101110 = 1 \times {2}^{5} + 0 \times {2}^{4} + 1 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1} + 0 \times {2}^{0} \\ = 32 + 0 + 8 + 4 + 2 + 0 \\ = 46 \\ b) : 101010 = 1 \times {2}^{5} + 0 \times {2}^{4} + 1 \times {2}^{3} + 0 \times {2}^{2} + 1 \times {2}^{1} + 0 \times {2}^{0} \\ = 32 + 0 + 8 + 0 + 2 + 0 \\ = 42 \\ c) : 111001 = 1 \times {2}^{5} + 1 \times {2}^{4} + 1 \times {2}^{3} + 0 \times {2}^{2} + 0 \times {2}^{1} + 1 \times {2}^{0} \\ = 32 + 16 + 8 + 0 + 0 + 1 \\ = 57 \\ d) : 000101 = 0 \times {2}^{5} + 0 \times {2}^{4} + 0 \times {2}^{3} + 1 \times {2}^{2} + 0 \times {2}^{1} + 1\times {2}^{0} = 0 + 0 + 0 + 4 + 0 + 1 \\ = 5$

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