Deep sleep is an experience of nothingness. It's not a blankness, buts an experience of blankness. All throughout consciousness, awareness is present. Notice it continues in deep sleep. You don't even think that i am sleeping, or this must be sleep, i am sleeping. When these are removed, we haven't said a single thing about consciousness. There is con usness. They're in deep sleep also, but alone, without an object,. Nothing objects to consciousness.
Inspired by the 15th chapter of the Ashtavakra Gita, Swami Sarvapriyananda gives a discourse on the nature of the Self.