1. The problem is to convert the number $1567_8$ from octal to decimal, then to binary, and finally to hexadecimal. 2. Convert $1567_8$ to decimal: Each digit represents a power of 8: $$1567_8 = 1 \times 8^3 + 5 \times 8^2 + 6 \times 8^1 + 7 \times 8^0$$ Calculate each term: $$1 \times 512 = 512$$ $$5 \times 64 = 320$$ $$6 \times 8 = 48$$ $$7 \times 1 = 7$$ Sum them up: $$512 + 320 + 48 + 7 = 887$$ So, $1567_8 = 887_{10}$. 3. Convert $887_{10}$ to binary: Divide by 2 repeatedly and record the remainders: $$887 \div 2 = 443 \text{ remainder } 1$$ $$443 \div 2 = 221 \text{ remainder } 1$$ $$221 \div 2 = 110 \text{ remainder } 1$$ $$110 \div 2 = 55 \text{ remainder } 0$$ $$55 \div 2 = 27 \text{ remainder } 1$$ $$27 \div 2 = 13 \text{ remainder } 1$$ $$13 \div 2 = 6 \text{ remainder } 1$$ $$6 \div 2 = 3 \text{ remainder } 0$$ $$3 \div 2 = 1 \text{ remainder } 1$$ $$1 \div 2 = 0 \text{ remainder } 1$$ Reading remainders from bottom to top, the binary is: $$1101110111_2$$ 4. Convert $887_{10}$ to hexadecimal: Divide by 16: $$887 \div 16 = 55 \text{ remainder } 7$$ $$55 \div 16 = 3 \text{ remainder } 7$$ $$3 \div 16 = 0 \text{ remainder } 3$$ Reading remainders from bottom to top: $$377_{16}$$ So, the final conversions are: Octal $1567_8 = Decimal 887_{10} = Binary 1101110111_2 = Hexadecimal 377_{16}$.