Which list correctly orders the following numbers from least to greatest: BIN: 1110, DEC: 13, HEX: F?

To determine the correct order of the numbers from least to greatest, it's essential to convert all numbers into the same base for easy comparison.

The binary number 1110 can be converted to decimal as follows:

• Each digit from the right represents a power of 2. Therefore, the binary value 1110 corresponds to:

• (1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 8 + 4 + 2 + 0 = 14)

Thus, the binary 1110 is equal to 14 in decimal.

Next, the hexadecimal number F corresponds to the decimal number 15. This is because in the hexadecimal system, the digits go from 0-9 followed by A (10), B (11), C (12), D (13), E (14), and F (15).

Now we can summarize the conversions:

• BIN 1110 = DEC 14

• DEC 13 = DEC 13

• HEX F = DEC 15

Ordering these decimal values from least to greatest gives us:

1. 13 (DEC)

2. 14 (BIN