How to count the bits in a Huffman tree

Question

I am looking at the below Huffman tree, the corresponding frequency table and the subtotal table. That table calculates the subtotal bits. I want to know how to count the subtotal bits.

In the first row of the subtotal table, code 0 maps to 15. I understand that because A has a count of 15. But why code 100 maps to 21? 100 represents the node B and B has a count of 7. I would think that for 100 we should calculate 7 + 15 = 22, but the table has 21. Why?

Answer 1

The column "Subtotal (#bits)" is the product of bit-length and count (frequency), and this represents how many bits in the encoded message are dedicated to represent all symbols B.

So we can derive the numbers as follows:

Symbol	Count	Code	#bits in Code	Subtotal (#bits)
A	15	0	1	15 x 1 = 15
B	7	100	3	7 x 3 = 21
C	6	101	3	6 x 3 = 18
D	6	110	3	6 x 3 = 18
E	5	111	3	5 x 3 = 15
				TOTAL = 87

87 is thus the length of the encoded message.