A system for purifying 1,3-butadiene, comprising: a first distillation column and a second distillation column, each column having a top portion, a bottom portion, and a middle portion; a first interconnection between the top portion of the first distillation column and the top portion of the second distillation column, wherein the first interconnection is configured to feed a liquid stream from the second distillation column to the first distillation column; a second interconnection between the bottom portion of the first distillation column and the bottom portion of the second distillation column, wherein the second interconnection is configured to feed a first gas stream from the second distillation column to the first distillation column; a top stream line configured to remove a second gas stream from the top portion of the second distillation column, wherein the top stream is coupled to a heat exchanger; a vapor outlet line connected to the heat exchanger to recover high volatility components from the second gas stream; a feed line for crude 1,3-butadiene to the first distillation column; a product outlet line for purified 1,3-butadiene from the second distillation column; a third interconnection between the top of the first distillation column and the top of the second column to feed a gas stream from the first column to the second column; and a fourth interconnection between the bottom of the first column to the bottom of the second column to feed liquid from the bottom of the first column to the bottom of the second column; wherein the second distillation column comprises 87 theoretical plates; and wherein the first distillation column has 30 theoretical plates. a first distillation column and a second distillation column, each column having a top portion, a bottom portion, and a middle portion; a first interconnection between the top portion of the first distillation column and the top portion of the second distillation column, wherein the first interconnection is configured to feed a liquid stream from the second distillation column to the first distillation column; a second interconnection between the bottom portion of the first distillation column and the bottom portion of the second distillation column, wherein the second interconnection is configured to feed a first gas stream from the second distillation column to the first distillation column; a top stream line configured to remove a second gas stream from the top portion of the second distillation column, wherein the top stream is coupled to a heat exchanger; a vapor outlet line connected to the heat exchanger to recover high volatility components from the second gas stream; a feed line for crude 1,3-butadiene to the first distillation column; a product outlet line for purified 1,3-butadiene from the second distillation column; a third interconnection between the top of the first distillation column and the top of the second column to feed a gas stream from the first column to the second column; and a fourth interconnection between the bottom of the first column to the bottom of the second column to feed liquid from the bottom of the first column to the bottom of the second column;