What is the binary representation for decimal 201?

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Study for the AAMI Certified Associate in Biomedical Technology Exam. Study with flashcards and multiple choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

What is the binary representation for decimal 201?

Explanation:
Binary representation expresses a number as a sum of powers of two. For decimal 201, identify which powers of two add up to 201: 201 = 128 + 64 + 8 + 1. Those correspond to 2^7, 2^6, 2^3, and 2^0 being 1, with all other bits being 0. Writing this in 8 bits gives 11001001, which indeed equals 128 + 64 + 8 + 1 = 201. The other binary strings add up to different totals (for example, 01000101 equals 64 + 4 + 1 = 69, 01011010 equals 64 + 16 + 8 + 2 = 90, and 00110010 equals 32 + 16 + 2 = 50).

Binary representation expresses a number as a sum of powers of two. For decimal 201, identify which powers of two add up to 201: 201 = 128 + 64 + 8 + 1. Those correspond to 2^7, 2^6, 2^3, and 2^0 being 1, with all other bits being 0. Writing this in 8 bits gives 11001001, which indeed equals 128 + 64 + 8 + 1 = 201. The other binary strings add up to different totals (for example, 01000101 equals 64 + 4 + 1 = 69, 01011010 equals 64 + 16 + 8 + 2 = 90, and 00110010 equals 32 + 16 + 2 = 50).

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