What is the binary equivalent of the unsigned decimal number 173?

2025

What is the binary equivalent of the unsigned decimal number 173?

  1. A.

    10101101

  2. B.

    10101100

  3. C.

    10101111

  4. D.

    10101011

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Correct answer: A

To convert the decimal number 173 to binary, we repeatedly divide by 2 and record the remainders. Dividing 173 by 2 gives a quotient of 86 and a remainder of 1. Continuing this process: 86 divided by 2 is 43 with remainder 0; 43 divided by 2 is 21 with remainder 1; 21 divided by 2 is 10 with remainder 1; 10 divided by 2 is 5 with remainder 0; 5 divided by 2 is 2 with remainder 1; and finally, 2 divided by 2 is 1 with remainder 0. Reading the remainders from bottom to top yields the binary sequence 10101101. Alternatively, you can sum powers of 2: 128 + 32 + 8 + 4 + 1 equals 173, which corresponds to bits set at positions 7, 5, 3, 2, and 0. Option B (10101100) is incorrect because it equals 172, missing the final unit. Option C (10101111) is incorrect as it sums to 175, adding extra value. Therefore, Option A represents the correct binary equivalent.

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