(0 × 2⁰) + (1 × 2⁻¹) + (1 × 2⁻²) + (0 × 2⁻³) + (1 × 2⁻⁴) =

asked by guest
on Oct 19, 2024 at 12:33 pm



You asked:

Evaluate the expression: \(0 \cdot {2}^{0} + 1 \cdot {2}^{-1} + 1 \cdot {2}^{-2} + 0 \cdot {2}^{-3} + 1 \cdot {2}^{-4}\)

MathBot Answer:

\[0 \cdot {2}^{0} + 1 \cdot {2}^{-1} + 1 \cdot {2}^{-2} + 0 \cdot {2}^{-3} + 1 \cdot {2}^{-4} = \frac{13}{16} = 0.8125\]

\[\begin{aligned}0 \cdot {2}^{0} + 1 \cdot {2}^{-1} + 1 \cdot {2}^{-2} + 0 \cdot {2}^{-3} + 1 \cdot {2}^{-4}& = 0 \cdot 2^{0} + \frac{1}{2} + 1 \cdot \frac{1}{2^{2}} + 0 \cdot \frac{1}{2^{3}} + 1 \cdot \frac{1}{2^{4}}\\& = 0 \cdot 1 + \frac{1}{2} + 1 \cdot \frac{1}{2^{2}} + 0 \cdot \frac{1}{2^{3}} + 1 \cdot \frac{1}{2^{4}}\\& = 0 + \frac{1}{2} + 1 \cdot \frac{1}{2^{2}} + 0 \cdot \frac{1}{2^{3}} + 1 \cdot \frac{1}{2^{4}}\\& = 0 + \frac{1}{2} + \frac{1}{4} + 0 \cdot \frac{1}{2^{3}} + 1 \cdot \frac{1}{2^{4}}\\& = 0 + \frac{1}{2} + \frac{1}{4} + \frac{0}{8} + 1 \cdot \frac{1}{2^{4}}\\& = 0 + \frac{1}{2} + \frac{1}{4} + 0 + 1 \cdot \frac{1}{2^{4}}\\& = 0 + \frac{1}{2} + \frac{1}{4} + 0 + \frac{1}{16}\\& = \frac{1}{2} + \frac{1}{4} + 0 + \frac{1}{16}\\& = \frac{3}{4} + 0 + \frac{1}{16}\\& = \frac{3}{4} + \frac{1}{16}\\& = \frac{13}{16}\end{aligned}\]

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