Biosignals such as electoencephalogram (EEG), electrocorticogram (ECoG), atrial electrogram (AEG) etc. are being recorded from multiple channels simultaneously to improve the spatial resolution of the signals. Conventional multichannel synchronous Analog-to-Digital Converters (ADCs) are used to convert the analog continuous time signals into discrete digital values. Several biosignals have a sparsity in time domain as they have fast-rising peaks in between periods of low activity. Use of conventional synchronous ADCs for conversion of such signals is not an efficient approach as their operation is constant, irrespective of the activity of the input signals. Asynchronous ADCs such as level-crossing (LC) ADCs exploit the sparsity of biosignals and thus their operation is activity-dependent. However, multichannel configurations of LC ADCs do not yet exist. This problem is investigated in this work and a new ADC architecture is presented that can combine synchronous sampling with level-crossing quantisation method while converting input signals from several channels simultaneously. The synchronous LC ADC presented in this work achieves 3.37 times reduction in quantisation steps and 6 times reduction in number of output bits generated during conversion of AEG signals as compared to conventional synchronous ADCs. The problem in existing LC ADCs of data overhead in adaptive resolution technique is solved through a novel method named split resolution technique which is also presented in this work.