Final answer:
The binary representation for the decimal number 47 is 0101111, which is option (a). This is calculated by summing the powers of 2 that equal to 47: 32 + 8 + 4 + 2 + 1.
Step-by-step explanation:
To determine which set of binary digits represents the number 47, we need to understand binary number system. The binary number system is base-2, meaning each digit represents a power of 2, starting with 20 on the far right. The digit positions are, from right to left, 20, 21, 22, 23, 24, 25, and 26 respectively which are 1, 2, 4, 8, 16, 32, 64, and so on.
To represent the decimal number 47 in binary, we find the combination of these powers of 2 that sum up to 47. The largest power of 2 less than 47 is 32 (25). After subtracting 32 from 47, we get 15. The next largest power of 2 less than 15 is 8 (23), which leaves us with 7. Continuing this, we get 4 (22) and 3 (20 + 21). The binary representation is therefore 1 at the positions for 32, 8, 4, 2, and 1, and 0 elsewhere.
The binary digits for the number 47 are: 0101111, which corresponds to the option (a).