Step 1: Know the standard.
IEEE 754 is the common rule computers follow to store real numbers in floating-point form.
Step 2: Recall its formats.
It defines single precision and double precision, each using a fixed number of bits.
Step 3: Focus on single precision.
Single precision splits its storage into three parts: a sign, an exponent, and a mantissa.
Step 4: List the bit counts.
Sign $= 1$ bit, exponent $= 8$ bits, mantissa $= 23$ bits.
Step 5: Add them together.
\[ 1 + 8 + 23 = 32 \]
Step 6: Match to the options.
So single precision uses $32$ bits, which is option (B). Double precision is the one that uses $64$ bits.
\[ \boxed{32 \text{ bits}} \]