This paper presents the design and implementation of two spiking neural network based sorting algorithms with time complexity of O(1). These algorithms are inspired from artificial neural network based sorting algorithms. A number comparator circuit using spiking network as a building block has been proposed and been used in the sorting algorithms to compare numbers. This comparator circuit is generic and can be used in other algorithms. Results show that both these algorithms take constant time to sort any count of numbers once the circuit is setup with sufficient input lines and input sequence of numbers is configured in the network.