In this letter, we propose an area-efficient series-connected resonant tunneling diode pair device (SCRTD) to utilize as a binary neuron device in cellular neural networks (CNNs). The proposed SCRTD (P-SCRTD) consists of two RTDs interconnected by a floating metal layer with a high-doped epitaxial layer. The P-SCRTD shows a 48 % reduction in area by eliminating the isolation area in the conventional SCRTD (C-SCRTD) owing to the symmetrical I-V characteristic of the RTD, without any performance penalty on the DC and RF characteristics by means of adopting the floating metal layer, compared to the C-SCRTD. CNN application of the P-SCRTD is investigated, showing inherent threshold operation and high-speed (12.5 Gbps) low-power (21 mW) performance, despite using the $2~\mu \text{m}$ technology node, for a unit cell for edge extraction.