1. Convert 262 to binary, octal, and hexadecimal: - Binary: Divide 262 by 2 repeatedly and record remainders: $$262 \div 2 = 131 \text{ remainder } 0$$ $$131 \div 2 = 65 \text{ remainder } 1$$ $$65 \div 2 = 32 \text{ remainder } 1$$ $$32 \div 2 = 16 \text{ remainder } 0$$ $$16 \div 2 = 8 \text{ remainder } 0$$ $$8 \div 2 = 4 \text{ remainder } 0$$ $$4 \div 2 = 2 \text{ remainder } 0$$ $$2 \div 2 = 1 \text{ remainder } 0$$ $$1 \div 2 = 0 \text{ remainder } 1$$ Reading remainders bottom to top: $100000110_2$ - Octal: Divide 262 by 8: $$262 \div 8 = 32 \text{ remainder } 6$$ $$32 \div 8 = 4 \text{ remainder } 0$$ $$4 \div 8 = 0 \text{ remainder } 4$$ Reading remainders bottom to top: $406_8$ - Hexadecimal: Divide 262 by 16: $$262 \div 16 = 16 \text{ remainder } 6$$ $$16 \div 16 = 1 \text{ remainder } 0$$ $$1 \div 16 = 0 \text{ remainder } 1$$ Reading remainders bottom to top: $106_{16}$ 2. Convert 305: - Binary: $305_{10} = 100110001_2$ - Octal: $305_{10} = 461_8$ - Hexadecimal: $305_{10} = 131_{16}$ 3. Convert 589: - Binary: $589_{10} = 1001001101_2$ - Octal: $589_{10} = 1115_8$ - Hexadecimal: $589_{10} = 24D_{16}$ 4. Convert 896: - Binary: $896_{10} = 1110000000_2$ - Octal: $896_{10} = 1600_8$ - Hexadecimal: $896_{10} = 380_{16}$ 5. Convert 1045: - Binary: $1045_{10} = 10000010101_2$ - Octal: $1045_{10} = 2045_8$ - Hexadecimal: $1045_{10} = 415_{16}$ Each conversion uses repeated division by the base and reading remainders from bottom to top.