Final answer:
To convert decimal numbers to base 2 (binary) or base 7, you can use a method of repeatedly dividing the decimal number by the base and recording the remainders in reverse order. To convert to base 16 (hexadecimal), divide by 16 and use letters for remainders greater than 9.
Step-by-step explanation:
To convert decimal numbers to base 2 (binary), we repeatedly divide the decimal number by 2 and record the remainders in reverse order. For example, to convert 17 to base 2, we divide 17 by 2 to get a quotient of 8 and a remainder of 1. Then we divide 8 by 2 to get a quotient of 4 and a remainder of 0. Finally, we divide 4 by 2 to get a quotient of 2 and a remainder of 0. The remainders in reverse order are 10001, so 17 in base 2 is 10001.
To convert decimal numbers to base 7, we follow a similar process. For example, to convert 17 to base 7, we divide 17 by 7 to get a quotient of 2 and a remainder of 3. Then we divide 2 by 7 to get a quotient of 0 and a remainder of 2. The remainders in reverse order are 23, so 17 in base 7 is 23.
To convert decimal numbers to base 16 (hexadecimal), we divide the decimal number by 16 and record the remainders in reverse order. However, when the remainder is greater than 9, we use the letters A, B, C, D, E, and F to represent the values 10, 11, 12, 13, 14, and 15, respectively. For example, to convert 17 to base 16, we divide 17 by 16 to get a quotient of 1 and a remainder of 1. The remainder is less than 10, so we represent it as 1. Therefore, 17 in base 16 is 11.