What is the binary equivalent of the unsigned decimal number 173?
2025
What is the binary equivalent of the unsigned decimal number 173?
- A.
10101101
- B.
10101100
- C.
10101111
- 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.