Output of a typical Wheatstone bridge, when it is connected to measure from a single or a dual resistive element, possesses non-linear characteristic. This paper presents a novel signal conditioning scheme, which provides a linear-digital output directly from the resistive sensor(s) that are connected in such bridge configurations. In the present scheme, the input stage of a dual-slope analog-to-digital converter (DSADC) is suitably augmented to incorporate the quarter-bridge and (or) half-bridge containing the resistive sensor as an integral part of the DSADC. A combination of the current mode excitation and wisely selected integration and de-integration operations of the DSADC enable to achieve linearization in the digitization process itself, leading to an overall reduction in the complexity level and number of blocks used keeping the high accuracy unaltered. A detailed analysis has been conducted to quantify the effect of various sources of errors in the output of the DSADC. The details are presented in the paper. The proposed method not only provides a linear digital output but also drastically reduces the effect on the output due to the lead wires that connect the Wheatstone bridge and the DSADC. Thus, the proposed scheme is well suited for the situations where the sensor(s) is (are) remotely located at a distance. Simulation studies as well as results from a prototype developed and tested establish the practicality of the proposed scheme. The inherent non-linearity of the Wheatstone bridge is reduced by nearly two orders of magnitude. © 2017 IEEE.