Carry free arithmetic using higher radix number system such as Redundant Binary Signed Digit can be used to meet the demand for computers operating at much higher speeds. The computation speed can also be increased by using the suitable design of adder and multiplier circuits. Fast RBSD adder cells suggested by Neelam Sharma in 2006 using universal logic are modified in the proposed design by reducing the number of gates. Due to reduction in gate count, number of gate levels and hence the circuit complexity is also reduced. As multiplication is repetitive addition, the implementation time of the multiplier circuit will also be reduced to a great extent by using modified design of adder cell to add the partial products. These partial products are added using pipelined units to reduce implementation time further. Thus with the use of proposed RBSD adder, other arithmetic operations such as subtraction, division, square root etc. can be performed much faster. It is concluded that efficiency of the proposed RBSD adder and multiplier is improved as compared to the techniques conventionally used in high speed machines. Thus the proposed modified RBSD adder cell using universal gates can be used to design fast ALU with many additional advantages.