1. The problem is to convert the hexadecimal number $\text{D42C3}_{16}$ into its binary equivalent. 2. Each hexadecimal digit corresponds to exactly 4 binary digits (bits). This is because hexadecimal is base 16 and binary is base 2, and $16 = 2^4$. 3. The hexadecimal digits and their binary equivalents are: - $D = 13_{10} = 1101_2$ - $4 = 4_{10} = 0100_2$ - $2 = 2_{10} = 0010_2$ - $C = 12_{10} = 1100_2$ - $3 = 3_{10} = 0011_2$ 4. Now, convert each digit: $$\text{D} = 1101$$ $$\text{4} = 0100$$ $$\text{2} = 0010$$ $$\text{C} = 1100$$ $$\text{3} = 0011$$ 5. Combine all binary groups in the same order: $$1101\,0100\,0010\,1100\,0011$$ 6. Therefore, the binary equivalent of $\text{D42C3}_{16}$ is: $$\boxed{11010100001011000011_2}$$