1- In recent work [1,13,19], researchers have shown the importance of energy minimization and its strong correlation with power.

2- work in [11, 15] proved that although the activity in the circuit may be the same, different combinations of power values still results in different energy values.

3- Many previous works targeted the minimization of energy which corresponds to number of positive power values for worst case vector pairs.

4- In [26,28], the authors have shown that amount of power drawn from supply voltage (and sunk to ground is different depending on the energy value.

5- For example, they have shown that a positive power value on the output draws approximately five times (5x) the current from power supply compared to that sunk to ground.

6- Alternately, a negative power value would result in current sunk to ground in access of 7x when compared to that drawn from the supply.

7- This means that the power plays a major role in the amount of energy consumed by the circuit , thus minimizing the number of positive power values only does not guarantee true minimum energy.

8- It can be seen from the results that power is reduced when using C-K concept when compared to the other approaches even for Y-M based ordering. For example, columns NM and HU both approaches have the same number of power (3), however, HU approach have lower power (2 for HU compared to 3 for NM approach).

9- In this work, we employed the C-K algorithm to reduce power by assigning Y bits suitable value of -1 or 1. Each Y in a vector is considered a node. Based on the initial random assignment value, all nodes associated with Y bits are placed in two partitions: 1-partition and -1-partition based on their initial fill value.

10- Algorithm HU is our implementation of filling algorithm that minimizes energy.

11- Then the newly selected vector becomes x, y is deleted from the unfilled list, and the process is repeated again.

12- In our framework, we initially randomly fill these Y bits then and reorder the input set, then we analyze these assignments for energy improvement and modify their assignments, when needed, to reduce energy.

13- Y Bits that were filled with -1 are placed in partition -1 whereas those filled with 1 are placed in partition 1

I hope that someone can help me to find and correct mistakes in my sentences
thanks alot