To convert a hexadecimal number to a binary number, we need to follow these steps:
Write down the hexadecimal number and assign a power of 16 to each digit, starting from the rightmost with 16^0.
Convert each hexadecimal digit to its decimal equivalent by multiplying it with its power of 16.
Add all the decimal values to get the decimal equivalent of the hexadecimal number.
Divide the decimal number by 2 repeatedly and write down the remainders from bottom to top.
The binary number is the sequence of remainders obtained in the previous step.
Let’s apply these steps to the hexadecimal number 17:
17 = 1 × 16^1 + 7 × 16^0
17 = 16 + 7
17 = 23 in decimal
23 / 2 = 11 with remainder 1
11 / 2 = 5 with remainder 1
5 / 2 = 2 with remainder 1
2 / 2 = 1 with remainder 0
1 / 2 = 0 with remainder 1
The binary number is 10111
Therefore, the binary equivalent of the hexadecimal number 17 is 10111 (option B).
References: The answer can be verified by using the following resources:
Hexadecimal to Binary Converter - Binary Hex Converters
How to Convert 17 from hexadecimal to binary - Calculator Online
Convert hexadecimal number 17 to binary - CoolConversion
17 in Binary - How to Convert 17 from Decimal to Binary? - Cuemath
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