he’s not a bit tired and he’s not a little tired

[diamondcutter]

One of my books says he’s not a bit tired means he’s not tired at all and he’s not a little tired means he’s very tired. Is that true?

The book’s name is Basic English Knowledge for Junior High School Students, by Xue Jinxing, Beijing Education Press, China

 

[tedmc]

Yes, that is true. They are indirect ways of saying the same things.

 

[Tarheel]

Both phrases in bold mean the same thing. He's not tired. Not even a little.

 

[diamondcutter]

Thanks, Tedmc and Tarheel.

Yes, that is true. They are indirect ways of saying the same things.

Hi, Tedmc.

Do you agree with the book or not? The book says the two sentences don’t have the same meaning.

 

[teechar]

One of my books says he’s not a bit tired means he’s not tired at all and he’s not a little tired means he’s very tired. Is that true?

Yes, that use of "not a little" is peculiar to British English. I don't think it's used in the American variety.
https://www.collinsdictionary.com/dictionary/english/not-a-little

 

[JMurray]

I agree with your reference book. The two phrases don't have the same meaning, as teechar's link explains.
For example, to say "He was not a little upset about the way things turned out", means that he was very upset.

 

[Tarheel]

Bob: He was not a little upset about the way things turned out.
Jack: On the contrary, he was very upset.
Bob: That's what I said.
Jack: No it isn't.
;-)

 

[Tdol]

Both phrases in bold mean the same thing. He's not tired. Not even a little.

In BrE, the latter is likely to mean that he is very tired.

 

[jutfrank]

Yes, this is a case of a particular rhetorical device that's common in British English at least—litotes.

 

[Tarheel]

Never forget the importance of context. Something than might be interpreted one way absent context may be seen entirely differently with that context.