What is the 4-bit binary representation of decimal 15?

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Multiple Choice

What is the 4-bit binary representation of decimal 15?

Explanation:
To represent a decimal number in binary, think in powers of two. For a 4-bit representation you have four positions corresponding to 8, 4, 2, and 1. The decimal 15 equals 8 + 4 + 2 + 1, so every one of these bit positions is a 1. Put together, that becomes 1111. The other patterns either correspond to different values (1010 is 10, 1110 is 14) or have more than four digits (11001), which isn’t allowed in a 4-bit form. So the 4-bit binary representation of 15 is 1111.

To represent a decimal number in binary, think in powers of two. For a 4-bit representation you have four positions corresponding to 8, 4, 2, and 1. The decimal 15 equals 8 + 4 + 2 + 1, so every one of these bit positions is a 1. Put together, that becomes 1111. The other patterns either correspond to different values (1010 is 10, 1110 is 14) or have more than four digits (11001), which isn’t allowed in a 4-bit form. So the 4-bit binary representation of 15 is 1111.

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