Discussion
The binary number 1101 is equivalent to which decimal value?
Answer: B
Correct answer: 13
Each binary digit carries a place value that is a power of two, read from the right: \( 2^{0}, 2^{1}, 2^{2}, 2^{3} \), that is 1, 2, 4 and 8. For 1101 the set bits are in the 8, 4 and 1 positions: \[ 1\times8 + 1\times4 + 0\times2 + 1\times1 = 8 + 4 + 1 = 13. \] The reverse conversion divides repeatedly by two and reads the remainders upward: 13 gives remainder 1, then 6 gives 0, then 3 gives 1, then 1 gives 1 - reading up, 1101. It is worth memorising the first few powers of two, since almost every question in this area rests on them: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Note also that 1101 is D in hexadecimal, since one hexadecimal digit covers exactly four bits - which is why hexadecimal is used as shorthand for binary.
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