What is the sum of the binary (base 2) number (1100)2 and the hexadecimal…
2022
What is the sum of the binary (base 2) number (1100)2 and the hexadecimal (base 16) number (3)16?
Answer: A. (F)16 — ConceptA positional numeral's value is the sum of each digit multiplied by its base raised to that digit's place. To add numbers written in different bases,…
- A.
(F)16
- B.
(15)16
- C.
(1003)10
- D.
(1103)5
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept
A positional numeral's value is the sum of each digit multiplied by its base raised to that digit's place. To add numbers written in different bases, first convert them to one common base.
Binary uses powers of 2, while hexadecimal uses powers of 16 and represents decimal values 10 through 15 by A through F.
Application
Convert the binary number: (1100)2 = 1×23 + 1×22 + 0×2 + 0 = 8 + 4 = 12 in decimal.
Convert the hexadecimal number: (3)16 = 3 in decimal.
Add in decimal: 12 + 3 = 15.
Convert 15 to hexadecimal: the single hexadecimal digit for decimal 15 is F, so the sum is (F)16.
Cross-check
Converting (F)16 back to decimal gives 15, which equals 12 + 3; therefore the conversion and addition agree.
Result: (F)16.