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To determine how many bits are needed to store the decimal number 1111, we first convert the decimal number into its binary equivalent. The decimal number 1111 can be expressed in binary as 10001010111, which requires 11 bits.

However, when looking solely at the value of the number 1111 itself, if we consider the highest value in the range of binary numbers that can be formed with a certain number of bits, we find that with 4 bits, the maximum number that can be represented is 15 (which is 1111 in binary). Therefore, at a minimum, 4 bits would be required to ensure that the binary representation can encompass all values up to and including 1111.

This aligns with the binary representation, where each bit can represent a power of 2. The binary counting up to 1111 goes as follows, starting at 1 (0001) and reaching 1111 (which is 15 in decimal). Hence, 4 bits are sufficient to represent the decimal number 1111 completely, as they are capable of covering all numbers from 0 to 15.

This understanding of binary counting and the relationship between decimal and binary systems leads to the conclusion that