Unless the number of each of those "billions" is only 2, then that's just about the entire human species.
Except that it wouldn't be. The people in remote rural areas would be the most likely to survive the initial blasts. They would also be the most likely to survive the ensuing economic disruption. If all the nukes in the world were detonated in maximum casualty producing air bursts, they would destroy about 0.2% of the Earth's land area. Air bursts produce minimal amounts of fallout. If they were detonated in sub-surface bursts (to destroy underground silos) the fallout would be worse, but would still mostly be contained in the ground locally, and almost no one would die in the initial bursts. Today's nukes are more efficient and cleaner than the WWII era bombs. They produce far less fallout for a given yield.
Even within target urban areas, there would be survivors. Some people in downtown Hiroshima, and many more in Nagasaki, survived the blast, and the radiation, and went on to have children and grandchildren. Most people in Hiroshima didn't die from the blast or the radiation. They died in the firestorm. But Nagasaki was mostly made from stone, instead of wood like Hiroshima, so there was no firestorm, and many more people survived there despite the bomb being nearly twice as powerful.
If people 200 meters from ground zero can survive, I am sure someone on New Zealand's South Island, 5000 km from the closest impact, will be okay.