"assigning" in the noun sense
1. assignment, assigning
the act of distributing something to designated places or persons
"the first task is the assignment of an address to each datum"
"assigning" in the verb sense
1. delegate, designate, depute, assign
give an assignment to (a person) to a post, or assign a task to (a person)
2. assign, allot, portion
"We were assigned new uniforms"
3. impute, ascribe, assign, attribute
attribute or credit to
"We attributed this quotation to Shakespeare"
"People impute great cleverness to cats"
4. assign, specify, set apart
select something or someone for a specific purpose
"The teacher assigned him to lead his classmates in the exercise"
5. put, assign
attribute or give
"She put too much emphasis on her the last statement"
"He put all his efforts into this job"
"The teacher put an interesting twist to the interpretation of the story"
6. arrogate, assign
make undue claims to having
transfer one's right to
8. assign, attribute
decide as to where something belongs in a scheme
"The biologist assigned the mushroom to the proper class"
Source: WordNet® (An amazing lexical database of English)
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