The Binary Omnius is the 1st omnius in the chain. It completely dwarfs The Gem of Toxicity in size. The second factor in the size is explained here:
You start off with 1. Multiply it by 10, and add 2. Multiply that by 10, and add 3. Multiply that by 10, and add 4. Go on until you reach adding a googol. That's the second factor in size. Each of these things have a core, which takes energy to hold the entire thing, and executes code to keep the thing stable. It also stores a centimeter-sized jail for extremely dangerous entities. Whenever an entity is sent to the jail, a request is sent to The Core of Everything to make the entity powerless and the size of a point. These cores have code, a code converter, and an LDI to do that.