Question

Convert binary to decimal. (2)

i. (101001)2 = (?)10

ii. (11011101)2 = (?)10​

Answer 1

Explanation:

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Answer 2

Explanation:

$(i) \: \: \: 101001 _{(2)} \\ = (1 \times {2}^{5} ) + (0 \times {2}^{4} ) + (1 \times {2}^{3} ) + (0 \times {2}^{2} ) + (0 \times {2}^{1} ) + (1 \times {2}^{0} ) \\ = (1 \times 32) + (0 \times 16) + (1 \times 8) + (0 \times 4) + (0 \times 2) + (1 \times 1) \\ = 32 + 0 + 8 + 0 + 0 + 1 \\ \boxed{ = \large \underline{ \underline{ 41 _{(10)}}}} \\ \\ (ii) \: \: \: 11011101 _{(2)} \\ = (1 \times {2}^{7} ) + (1 \times {2}^{6} ) + (0 \times {2}^{5} ) + (1 \times {2}^{4} ) + (1 \times {2}^{3} ) + (1 \times {2}^{2} ) + (0 \times {2}^{1} ) + (1 \times {2}^{0} ) \\ = (1 \times 128) + (1 \times 64) + (0 \times 32) + (1 \times 16) + (1 \times 8) + (1 \times 4) + (0 \times 2) + (1 \times 1) \\ = 128 + 64 + 0 + 16 + 8 + 4 + 0 + 1 \\ \boxed{ = \large \underline{ \underline{ 221 _{(10)}}}}$