YOU SAID:

I am a bit tired and I would not mind sleeping a bit

INTO JAPANESE

私は少し疲れていて、少し寝てもかまいません

BACK INTO ENGLISH

I'm a little tired and can sleep a little

INTO JAPANESE

私は少し疲れていて、少し眠ることができます

BACK INTO ENGLISH

I'm a little tired and can sleep a little