2. (a) How many possible 4-Cbit states are there? (b) Express all of the 4-Cbit states using the long form of the Dirac notation and binary integers. (c) Write all of the 4-Cbit states using the compact form of the Dirac no- tation and binary integers. (d) Expres the 4-Cbit states using Dirac notation and decimal integers. 3. (a) If lo > and |1 . express 11 > as the tensor product of these unit vectors. (b) Write |11> as a column vector having 16 binary integer components. 4. Let S,, and Cij be the SWAP and the cNOT operators on a 3-Cbit space. (a) Determine the 8x8 matrices representing S1s and S31 How do they compare? (b) Determine the 8x8 matrices representing Cis and Csi. How do they compare? 2. (a) How many possible 4-Cbit states are there? (b) Express all of the 4-Cbit states using the long form of the Dirac notation and binary integers. (c) Write all of the 4-Cbit states using the compact form of the Dirac no- tation and binary integers. (d) Expres the 4-Cbit states using Dirac notation and decimal integers. 3. (a) If lo > and |1 . express 11 > as the tensor product of these unit vectors. (b) Write |11> as a column vector having 16 binary integer components. 4. Let S,, and Cij be the SWAP and the cNOT operators on a 3-Cbit space. (a) Determine the 8x8 matrices representing S1s and S31 How do they compare? (b) Determine the 8x8 matrices representing Cis and Csi. How do they compare