I think you can use:
df['Col3'] = 'XX'
df.loc[(df.Col1 == 'A') & (df.Col2 == 1), 'Col3'] = 'A1'
df.loc[(df.Col1 == 'A') & (df.Col2 == 0), 'Col3'] = 'A0'
With double numpy.where:
df["Col3"] = np.where((df.Col1 == 'A') & (df.Col2 == 1) , "A1",
np.where((df.Col1 == 'A') & (df.Col2 == 0), 'A0', 'XX'))
Sample:
df = pd.DataFrame({'Col1':['A','B','A','B'],
'Col2':[1,1,0,0]})
print (df)
Col1 Col2
0 A 1
1 B 1
2 A 0
3 B 0
df['Col3'] = 'XX'
df.loc[(df.Col1 == 'A') & (df.Col2 == 1), 'Col3'] = 'A1'
df.loc[(df.Col1 == 'A') & (df.Col2 == 0), 'Col3'] = 'A0'
df["Col4"] = np.where((df.Col1 == 'A') & (df.Col2 == 1) , "A1",
np.where((df.Col1 == 'A') & (df.Col2 == 0), 'A0', 'XX'))
print (df)
Col1 Col2 Col3 Col4
0 A 1 A1 A1
1 B 1 XX XX
2 A 0 A0 A0
3 B 0 XX XX