A double digital option is a particular variety of option

Option (finance)

In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

 (a financial derivative). At maturity, the payoff is 1 if the spot price of the underlying asset is between two numbers, the lower and upper strikes of the option; otherwise, it is 0.

A double digital with lower strike K₁ and upper strike K₂ can be replicated by going long a digital option

Binary option

In finance, a binary option is a type of option where the payoff is either some fixed amount of some asset or nothing at all. The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option...

with strike K₁ and short another digital option with strike K₂.