What is the binary equivalent of the decimal number 15?

Question

BlackTom AI · Accepted Answer

We start by restating the task: convert the decimal number 15 to binary and evaluate each provided option.
Option a: 1100₂. This binary value corresponds to 1×8 + 1×4 + 0×2 + 0×1 = 8 + 4 = 12 in decimal, so it does not equal 15.
Option b: 1010₂. This equals 1×8 + 0×4 + 1×2 + 0×1 = 8 + 2 = 10, which is not 15.
Option c: 0111₂. Interpreting this as 0×8 + 1×4 + 1×2 + 1×1 = 0 + 4 + 2 + 1 = 7. The leading zero does not change the value, so this is still 7, not 15.
Option d: 1000₂. This is 1×8 + 0×4 + 0×2 + 0×1 = 8, which is far from 15.
Option e: 1111₂. This equals 1×8 + 1×4 + 1×2 + 1×1 = 8 + 4 + 2 + 1 = 15, which matches the target decimal value.
Thus, the option that correctly represents 15 in binary is the one showing 1111₂, since summing the place values for each 1 bit yields 15. The other choices either overcount or undercount the bit contributions, leading to decimal results that are not 15.

System Software and Computing Concepts (032025-NHM)

What is the binary equivalent of the decimal number 15?

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