## Discuss the bit-serial processing elements.

Ans. The possibility for placing n parallel processing stages on a single silicon die is dim for large value of n, even as integrated circuit technology scales to smaller dimensions. Typically, the size of the processing stages and the interconnection buses need too much silicon area. Bit-serial processing stages are employed partial solution of this problem. These stages are smaller compare to their m-bit parallel counterparts by at least a factor of m, permitting m times as many stages to be placed on a silicon die. Thereby avoiding inter connection buses, if the processing stages are designed suitably. Individual stages time and silicon area, this method of interconnection by default is used within integrated circuit design.

At the initial stage, the bit-serial processing stages are a factor of 1/m as fast as stages of parallel processing. This could negate the gain obtained by placing m time as many processors on a silicon die. Although, bit-serial multipliers and adders are used to remove carry propagation delay. This gives a advantage of net processing speed when m-bit –serial processing stages replace a single stage of m-bit parallel processing.

Fig. 4.16 shows an example of a simple bit-serial multiplier. The multiplicand b in parallel and the multiplier a in bit-sequential form are necessary for this particular bit-serial multiplier algorithm. During the first iteration, the first bit of the multiplier a_{0} is input and ANDed with the parallel multiplicand b, generating a set of variable known as summands. The summands are added by the full adders to determine a set of partial product bit and the first product bit P_{0}. Carries and partial product bits are stored and moved through unit delay registers therefore they are present for the next step. It is ANDed with the multiplicand and added to previous carries and partial product bits, as the second multiplier bit a_{1} is moved in. this generates a second bit of the product P_{1}. The weight of each stage doubles at each iteration, giving the carry to be feedback within the same stage. This operation continues until the multiplier a is exhausted and the whole product has been moved out of the multiplier