If a number is written with its base shown as a subscript, identify the correct descending order of the following numbers 1-4 when converted to the decimal number system. A. (103.2) in base 4; B. (100011.11) in base 2; C. (46.2) in base 8; D. (36.6) in base 16. Choose the correct answer from the options given below:
1.2) in base 4
2.11) in base 2
3.2) in base 8
4.6) in base 16
A2, 3, 4, 1
B4, 1, 2, 3
C3, 4, 2, 1
D4, 3, 2, 1 ✓ Correct
Correct answer: (D) 4, 3, 2, 1
Explanation
Converting each number to decimal shows number 4 is the largest at 54.375, so the descending order begins with it.
Number 4, (36.6) in base 16, equals 54.375 in decimal, the highest value here.
Number 3, (46.2) in base 8, equals 38.25, placing it second.
Number 2, (100011.11) in base 2, equals 35.75, placing it third.
Number 1, (103.2) in base 4, equals 19.5, the smallest value.
The correct descending order is therefore 4, 3, 2, 1.
A higher base packs more value into each digit position than a lower base.
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