Among the statements about how computers represent numbers, the following is true:
- Computers represent numbers using a fixed number of bits, which limits the range of numbers they can represent. As a result, some numbers are too large to represent within this fixed bit-length, leading to overflow errors
Additional relevant details:
- Computers use the binary (base-2) number system internally because their hardware components operate in two states (on and off)
- Integers are represented using fixed bit-lengths such as 8, 16, 32, or 64 bits. Signed integers (which can represent negative numbers) use schemes like sign-magnitude, ones' complement, or two's complement, with two's complement being the most common in modern systems
- Floating-point representation is used to approximate real numbers and handle a wider range than fixed-length integers. This uses a form similar to scientific notation with a significand and exponent, typically following the IEEE 754 standard
- Increasing the number of bits can reduce round-off error and increase precision but cannot completely eliminate overflow errors because the number of representable values remains finite
In summary, the key true statement is that with a fixed number of bits, some numbers are too large to represent, which can cause overflow errors in computers.
