1. The problem is to convert the binary number $10111.101$ into the decimal number system. 2. The formula to convert a binary number to decimal is to sum each digit multiplied by $2$ raised to the power of its position index, counting from right to left for the integer part starting at 0, and from left to right for the fractional part starting at $-1$. 3. For the integer part $10111$, label the positions as follows: $1\times2^4 + 0\times2^3 + 1\times2^2 + 1\times2^1 + 1\times2^0$. 4. Calculate each term: $$1\times2^4 = 16$$ $$0\times2^3 = 0$$ $$1\times2^2 = 4$$ $$1\times2^1 = 2$$ $$1\times2^0 = 1$$ 5. Sum the integer part: $$16 + 0 + 4 + 2 + 1 = 23$$ 6. For the fractional part $.101$, label the positions as follows: $1\times2^{-1} + 0\times2^{-2} + 1\times2^{-3}$. 7. Calculate each term: $$1\times2^{-1} = \frac{1}{2} = 0.5$$ $$0\times2^{-2} = 0$$ $$1\times2^{-3} = \frac{1}{8} = 0.125$$ 8. Sum the fractional part: $$0.5 + 0 + 0.125 = 0.625$$ 9. Add the integer and fractional parts to get the decimal number: $$23 + 0.625 = 23.625$$ Therefore, the binary number $10111.101$ in decimal is $23.625$.