1. The problem is to convert the decimal number 97.4375 to its binary equivalent. 2. To convert a decimal number to binary, we convert the integer part and the fractional part separately. 3. Convert the integer part 97 to binary by dividing by 2 and recording remainders: $$97 \div 2 = 48 \text{ remainder } 1$$ $$48 \div 2 = 24 \text{ remainder } 0$$ $$24 \div 2 = 12 \text{ remainder } 0$$ $$12 \div 2 = 6 \text{ remainder } 0$$ $$6 \div 2 = 3 \text{ remainder } 0$$ $$3 \div 2 = 1 \text{ remainder } 1$$ $$1 \div 2 = 0 \text{ remainder } 1$$ Reading remainders from bottom to top gives integer binary: $$1100001_2$$ 4. Convert the fractional part 0.4375 to binary by multiplying by 2 and taking the integer parts: $$0.4375 \times 2 = 0.875 \rightarrow 0$$ $$0.875 \times 2 = 1.75 \rightarrow 1$$ $$0.75 \times 2 = 1.5 \rightarrow 1$$ $$0.5 \times 2 = 1.0 \rightarrow 1$$ The fractional binary is the sequence of integer parts: $$0111_2$$ 5. Combine integer and fractional parts: $$97.4375_{10} = 1100001.0111_2$$ This is the binary representation of 97.4375.