4 bit adder(SN74LS283N) not working properly
I know that 10k resistors may be too much


Yes, they are too much. An LSTTL input may go to several internal diodes and/or transistors which are operated by drawing current from them. The input voltage should be below 0.8 V for a 'low' (logic '0'), so the pull down resistance must be low enough to drop less than 0.8 V at the specified input current. 74LS283 A and B inputs may source up to 0.8 mA, so the maximum resistance that guarantees logic '0' is 0.8 V / 0.8 mA = 1 k&ohm;.

Other logic types have different current requirements depending on the semiconductors used and internal operating currents. Most modern logic IC's use MOSFETs which are driven by voltage and require negligible DC input current, so very high resistor values can be used. This also applies to the older CD4000 and 74HC series, and NMOS LSI chips.