In-Memory Wallace Tree Multipliers Based on Majority Gates Within Voltage-Gated SOT-MRAM Crossbar Arrays

In-memory computing represents an efficient paradigm for high-performance computing using crossbar arrays of emerging nonvolatile devices. While various techniques have emerged to implement Boolean logic in memory, the latency of arithmetic circuits, particularly multipliers, significantly increases with bit-width. In this work, we introduce an in-memory Wallace tree multiplier based on majority gates within voltage-gated spin-orbit torque (SOT) magnetoresistive random access memory (MRAM) crossbar arrays. By utilizing a resistance sum, the majority gate is implemented during READ operations in voltage-gated SOT-MRAM crossbar arrays, resulting in reduced read currents and improved energy efficiency. We employ a series of READ and WRITE operations to perform multiplier calculations, leveraging the fast READ and WRITE speeds of voltage-gated SOT-MRAM devices. Furthermore, the use of five-input majority gates simplifies multiplication by employing uniform logic gates and reducing logic depth, thereby lowering the operation’s complexity and the total number of occupied cells. Our experimental results demonstrate that the proposed in-memory Wallace tree multipliers consume three times less energy for in-memory operations than previously reported 4 $\times$ $4$ multipliers. Moreover, the proposed method reduces the delay overhead from O ( $n^{2}$ ) to O ( $\log_{2}{n}$ ), where $\mathit{n}$ represents the number of bits.