Digital computers are built using electronic components that have two reliable physical states, such as on and off or high and low voltage. The binary system with digits 0 and 1 maps directly to these two states. This makes hardware design, signal detection, and noise tolerance much easier. Therefore, binary is preferred because its symbols align naturally with underlying physical behavior.
Option A:
Option A is incorrect because binary cannot represent all decimal fractions exactly with a finite number of bits. Many decimal fractions have repeating binary expansions. The main reason for using binary is hardware compatibility, not perfect fractional representation.
Option B:
Option B correctly identifies the key advantage of binary for digital systems. Each bit corresponds to a physical state, like presence or absence of current. This direct mapping simplifies circuitry, improves reliability, and makes binary arithmetic practical in real machines.
Option C:
Option C is misleading because binary sometimes uses more digits than decimal for the same value. For example, 15 is shorter in decimal than in binary. The preference for binary is not about digit count but about ease of hardware implementation.
Option D:
Option D claims that binary eliminates all rounding errors, which is false. Binary floating-point formats still incur rounding when representing many real numbers. Rounding errors come from finite precision, not from the choice of base alone.
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