Equation in binary numbers. If 23n =1111 base 2, find n

September 25, 2026Computer Science

ScanSolve AI Answer

Answer

n = \frac{15}{23}

2 steps

Convert the binary number $1111_2$ to base 10.
$1111_2 = 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$ $1111_2 = 1 \times 8 + 1 \times 4 + 1 \times 2 + 1 \times 1$ $1111_2 = 8 + 4 + 2 + 1$ $1111_2 = 15_{10}$
Substitute the base 10 value into the equation and solve for $n$ .
$23n = 15$ $n = \frac{15}{23}$
The value of $n$ is $\frac{15}{23}$ .

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