Long number bit-serial squarers

New bit serial squarers for long numbers in LSB first form, are presented in this paper. The first presented scheme is a 50% operational efficient squarer than has the half number of cells compared to the traditional squarers. The second scheme is a 100% operational efficient squarer. In this scheme, the number of the cells remain unchanged compared to other proposed schemes but the number of the required registers is reduced significantly. Both schemes are presented in non-systolic and systolic form and are compared against other squarers presented in the bibliography from the aspect of hardware complexity.