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 from bottom to top: $100000110_2$ - Octal: Divide 262 by 8 repeatedly: $$262 \div 8 = 32 \text{ remainder } 6$$ $$32 \div 8 = 4 \text{ remainder } 0$$ $$4 \div 8 = 0 \text{ remainder } 4$$ Reading remainders from bottom to top: $406_8$ - Hexadecimal: Divide 262 by 16 repeatedly: $$262 \div 16 = 16 \text{ remainder } 6$$ $$16 \div 16 = 1 \text{ remainder } 0$$ $$1 \div 16 = 0 \text{ remainder } 1$$ Reading remainders from bottom to top: $106_{16}$ 2. Convert 305: - Binary: $$305 \div 2 = 152 \text{ remainder } 1$$ $$152 \div 2 = 76 \text{ remainder } 0$$ $$76 \div 2 = 38 \text{ remainder } 0$$ $$38 \div 2 = 19 \text{ remainder } 0$$ $$19 \div 2 = 9 \text{ remainder } 1$$ $$9 \div 2 = 4 \text{ remainder } 1$$ $$4 \div 2 = 2 \text{ remainder } 0$$ $$2 \div 2 = 1 \text{ remainder } 0$$ $$1 \div 2 = 0 \text{ remainder } 1$$ Binary: $100110001_2$ - Octal: $$305 \div 8 = 38 \text{ remainder } 1$$ $$38 \div 8 = 4 \text{ remainder } 6$$ $$4 \div 8 = 0 \text{ remainder } 4$$ Octal: $461_8$ - Hexadecimal: $$305 \div 16 = 19 \text{ remainder } 1$$ $$19 \div 16 = 1 \text{ remainder } 3$$ $$1 \div 16 = 0 \text{ remainder } 1$$ Hexadecimal: $131_{16}$ 3. Convert 589: - Binary: $$589 \div 2 = 294 \text{ remainder } 1$$ $$294 \div 2 = 147 \text{ remainder } 0$$ $$147 \div 2 = 73 \text{ remainder } 1$$ $$73 \div 2 = 36 \text{ remainder } 1$$ $$36 \div 2 = 18 \text{ remainder } 0$$ $$18 \div 2 = 9 \text{ remainder } 0$$ $$9 \div 2 = 4 \text{ remainder } 1$$ $$4 \div 2 = 2 \text{ remainder } 0$$ $$2 \div 2 = 1 \text{ remainder } 0$$ $$1 \div 2 = 0 \text{ remainder } 1$$ Binary: $1001001101_2$ - Octal: $$589 \div 8 = 73 \text{ remainder } 5$$ $$73 \div 8 = 9 \text{ remainder } 1$$ $$9 \div 8 = 1 \text{ remainder } 1$$ $$1 \div 8 = 0 \text{ remainder } 1$$ Octal: $1115_8$ - Hexadecimal: $$589 \div 16 = 36 \text{ remainder } 13$$ (D in hex) $$36 \div 16 = 2 \text{ remainder } 4$$ $$2 \div 16 = 0 \text{ remainder } 2$$ Hexadecimal: $24D_{16}$ 4. Convert 896: - Binary: $$896 \div 2 = 448 \text{ remainder } 0$$ $$448 \div 2 = 224 \text{ remainder } 0$$ $$224 \div 2 = 112 \text{ remainder } 0$$ $$112 \div 2 = 56 \text{ remainder } 0$$ $$56 \div 2 = 28 \text{ remainder } 0$$ $$28 \div 2 = 14 \text{ remainder } 0$$ $$14 \div 2 = 7 \text{ remainder } 0$$ $$7 \div 2 = 3 \text{ remainder } 1$$ $$3 \div 2 = 1 \text{ remainder } 1$$ $$1 \div 2 = 0 \text{ remainder } 1$$ Binary: $1110000000_2$ - Octal: $$896 \div 8 = 112 \text{ remainder } 0$$ $$112 \div 8 = 14 \text{ remainder } 0$$ $$14 \div 8 = 1 \text{ remainder } 6$$ $$1 \div 8 = 0 \text{ remainder } 1$$ Octal: $1600_8$ - Hexadecimal: $$896 \div 16 = 56 \text{ remainder } 0$$ $$56 \div 16 = 3 \text{ remainder } 8$$ $$3 \div 16 = 0 \text{ remainder } 3$$ Hexadecimal: $380_{16}$ 5. Convert 1045: - Binary: $$1045 \div 2 = 522 \text{ remainder } 1$$ $$522 \div 2 = 261 \text{ remainder } 0$$ $$261 \div 2 = 130 \text{ remainder } 1$$ $$130 \div 2 = 65 \text{ remainder } 0$$ $$65 \div 2 = 32 \text{ remainder } 1$$ $$32 \div 2 = 16 \text{ remainder } 0$$ $$16 \div 2 = 8 \text{ remainder } 0$$ $$8 \div 2 = 4 \text{ remainder } 0$$ $$4 \div 2 = 2 \text{ remainder } 0$$ $$2 \div 2 = 1 \text{ remainder } 0$$ $$1 \div 2 = 0 \text{ remainder } 1$$ Binary: $10000010101_2$ - Octal: $$1045 \div 8 = 130 \text{ remainder } 5$$ $$130 \div 8 = 16 \text{ remainder } 2$$ $$16 \div 8 = 2 \text{ remainder } 0$$ $$2 \div 8 = 0 \text{ remainder } 2$$ Octal: $2025_8$ - Hexadecimal: $$1045 \div 16 = 65 \text{ remainder } 5$$ $$65 \div 16 = 4 \text{ remainder } 1$$ $$4 \div 16 = 0 \text{ remainder } 4$$ Hexadecimal: $415_{16}$