Final answer:
Binary digits, or bits, are needed to represent a number in computers. For integer 321, at least 9 bits are required. Floating-point representation, which includes both significant figures and an exponent, uses formats like IEEE 754 and requires more bits, typically 32 or 64.
Step-by-step explanation:
The question revolves around the concept of representing a number using binary digits, also known as bits. When dealing with fixed values, the exact number of bits depends on whether we're representing the number in integer form or if a floating-point representation is used. As the value given is 321.4, this would typically be represented in a computer using floating-point representation, which can handle decimal values and uses a specific number of bits for the mantissa (significant figures) and exponent in a standard format like IEEE 754. In the IEEE 754 format, common sizes for floating points are 32 bits (single precision) and 64 bits (double precision).
However, if we were to simplify and assume we only wished to represent the integer part, 321 in binary would require 9 bits, as 28 (256) is the largest power of 2 less than 321 and we would need one additional bit to make up the difference to reach 321. However, this simplification does not account for the decimal part (0.4), which would require additional bits and a more complex representation to deal with the fractional part.
Regarding significant figures and scientific notation, it is also important that when doing mathematical operations, the result should be reported with the correct number of significant figures. For example, if a calculation yields a result like 0.4071661238 but the input numbers had three significant figures, the result should be rounded appropriately, reflecting the precision of the input values. Similarly, when expressing numbers in scientific notation, the number of significant figures should match those of the original number.