Neuromorphic computing describes the use of VLSI systems to mimic neuro-biological architectures and is also looked at as a promising alternative to the traditional von Neumann architecture. Any new computing architecture would need a system that can perform floating-point arithmetic. In this paper, we describe a neuromorphic system that performs IEEE 754-compliant floating-point multiplication. The complex process of multiplication is divided into smaller sub-tasks performed by components Exponent Adder, Bias Subtractor, Mantissa Multiplier and Sign OF/UF. We study the effect of the number of neurons per bit on accuracy and bit error rate, and estimate the optimal number of neurons needed for each component.