Question

Convert the hexadecimal expansion of each of the following integers to a binary expansion.

a. (ABBA)₁₆

Answer 1

To convert (ABBA)16 to a binary expansion, each hexadecimal digit is converted to its four-bit binary equivalent: A converts to 1010 and B converts to 1011. Combining the conversions in order gives us 1010 1011 1011 1010 in binary.

Step-by-step explanation:

To convert the hexadecimal expansion of the integer (ABBA)16 to a binary expansion, we need to convert each hexadecimal digit to its binary equivalent, which is a four-bit binary number.

Step-by-step Conversion:

1. Convert 'A' to binary: A in hexadecimal is 10 in decimal, so in binary it is 1010.
2. Convert 'B' to binary: B in hexadecimal is 11 in decimal, so in binary it is 1011. This is done twice since we have two 'B's.
3. Convert the final 'A' to binary: Again, A in hexadecimal is 10 in decimal, so in binary it is 1010.

Now, we combine all the binary digits in the order they appear in the hexadecimal number to get the final binary expansion:

(ABBA)16 = 1010 1011 1011 10102