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.

What is the binary equivalent of the decimal number 15?单项选择题

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