Question

Add the numbers (base 2): (1.01) * (2^3) + (1.11) * (2^1)

Answer 1

Answer:

1.01 * 8 + 1.11 * 2

8.08 + 2.22

10.30

hope it may helpful

Answer 2

Explanation:

Given:

(base 2): (1.01) * (2³) + (1.11) * (2^1)

To find: Addition

Solution:

To simplify the expression

first convert 2³ and 2 in binary i.e. base 2

${2}^{3} = 8 = (1000)_2 \\ 2 = (10)_2$

Multiply

$(1.01)_2\times (1000)_2 \\ = > \\ 1.01 \\ \times 1000 \\ - - - - \\ \: \: \: \: \: \: \: \: \: 000 \\ \: \: \: \: \: \: \: 000 \times \\ \: \: \: 000 \times \times \\ 101 \times \times \times \\ - - - - - - \\ (1010.00)_2 \\ - - - - -$

Multiply

$(1.11)_2 \times (10)_2 \\ \\ 1.11 \\ \times 10 \\ - - - - \\ \: \: \: 000 \\ 111 \times \\ - - - - - \\ (11.10)_2 \\ - - - -$

Now add both

$(1010.00)_2 \\ \: + (11.10)_2 \\ - - - - - \\ (1101.10)_2 \\ - - - -$

Thus,

$(1.01) \times (2^3) + (1.11) \times (2^1)=(1101.10)_2$

Hope it helps you.

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