AQA · GCSE · Computer Science · Higher

Huffman versus ASCII savings calculation

Q09.2 3 marks

Table 1 shows the Huffman codes for the characters used in the string HESELLSSEASHELLASHES.

Table 1

Character	Character frequency	Huffman code
S	6	11
E	5	10
L	4	00
H	3	011
A	2	010
	20

Calculate how many bits would be saved if the string HESELLSSEASHELLASHES was encoded using the Huffman codes shown in Table 1, rather than using ASCII.

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Marking points

1 Calculates or clearly attempts the Huffman total from character frequencies and code lengths.
2 Calculates or clearly attempts the 7-bit ASCII total for 20 characters.
3 Subtracts Huffman bits from ASCII bits to find the saving.

Full-mark answer

Huffman: (6×2) + (5×2) + (4×2) + (3×3) + (2×3) = 45 bits. ASCII: 20×7 = 140 bits. Bits saved = 140−45 = 95 bits.

Why this answer loses marks

I calculated the Huffman total and called it the saving.

A saving is a comparison: calculate the ASCII baseline too, then take the difference between the totals.

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