The Huffman code for the provided probabilities is constructed by iteratively combining the two symbols with the lowest probabilities until a single symbol remains. In this case:

$1.$ Combine B and D to create BD $($P$($BD$)=1/4).$

$2.$ Combine A and BD to create ABD $($P$($ABD$)=1/2).$

$3.$ Combine ABD and C to form the final code $($P$($ABD$)+$ P$($C$)=1).$

The resulting Huffman code is A: $10,$ B: $00,$ D: $01,$ C: $1.$ This code is uniquely decodable and efficient, assigning shorter codewords to more probable symbols