Spiking neural networks (SNNs) can achieve lower latency and higher efficiency compared with traditional neural networks if they are implemented in dedicated neuromorphic hardware. In both biological and artificial spiking neuronal systems, synaptic modifications are the main mechanism for learning. Plastic synapses are thus the core component of neuromorphic hardware with on‐chip learning capability. Recently, several research groups have designed hardware architectures for modeling plasticity in SNNs for various applications. Following these research efforts, this paper proposes multiplier‐less digital neuromorphic circuits for two plasticity learning rules: the spike‐driven synaptic plasticity (SDSP) and synaptic strength–based spike timing–dependent plasticity (SSSTDP). The proposed architectures have increased the precision of the plastic synaptic weights and are suitable for spiking neural network architectures with more precise calculations. The proposed models are validated in MATLAB simulations and physical implementations on a field‐programmable gate array (FPGA).