This spoiler does reveal the ending to halo 4, you have been warned!
Okay so I completed the game and I can’t help feeling slightly confused. Firstly where we’re the chief and cortana after the nuke explosion? And also how the hell did cortana save him?! Did she use her rampant beings to shield him like she did to attack the diadect?
They were in Earth orbit, she manipulated the light bridge to shield him and so she could touch him. As for what happened to her is you search the forums there are atleast 2 theories as to how she could have survived.
Cortana used her last energy to create a shield around Chief to save him from the blast, she then turned into her human-size form to touch the Chief, which she had been waiting to do. Truly sad 
I can nearly guarantee she’s not dead, though. The story was just getting really interesting with her, and Chief made a promise…
cortana was the hardlight bridge they were standing on
she shielded chief with it
she used the hardlight and made it into a shape of herself to touch chief at the end as well as to “grab” diadact
Yeah I thought that but it didn’t really make it too clear, but looking back now it all makes sense. Yeah I think cortana is definitely coming back. A lot of people are mentioning that she may even been made Into a human, as the forerunners could turn humans to AI’s e.g 343 guilty spark, however it may also be possible to reverse the action, allowing cortana to become human.