Question

9. (4) Select the best choice as Huffman code for the following symbols and their probabilities: A-0.10 C-0.17 E-0.21 B-0.21 D-0.06 F-0.25 (a) A: O, B: 10, C: 110, D: 1110, E: 11110, F: 11111 (b) A: 0,B: 10, C: 11111, D: 1110, E: 11110, F: 110 (c) A: 11110, B: 10, C: 1110, D: 11111, E: 110, F: 0 (d) A: 11111, B: 11110, C: 1110, D: 110, E: 10, F: 0 (e) A: 0,B: 01, C: 0001, D: 00000, E: 001, F: 1 (f) A: 101, B: 011, F: 001, D: 0, E: 0111, C: 1111 8) A: 1111, B: 0111, F:0, D: 011, E:101 (h) A: 1111, B: 100, F: 0, D: 1110, E: 101, C: 110 (i) A: 0000, B: 011, F: 0, D: 0001, E: 010, C: 001 6) A: 1110, B: 100, C: 110, D: 1111, E: 101, F: 0 (k) A: 11111, B: 10, F: 0, D: 11110, E: 110, C: 1110 (0) None of the above 10. (4) Find the average code length of the codes above. (a) 1 bit (b) 2 bits (c) 2.28 bits (d) 2.78 bits (e) 3 bits (f) 3.41 bits (g) 3.57 bits (h) 4 bits (i) none of the above 11. (4) What is the entropy of the letters listed in 9. above in bits? (a) 1 (b) 2 (c) 2.45 (d) 3 (e) 13.35 (0) None of the above

Answer 1

A →0. 10 B70.21 F=0.25 D40 06 9 TO tind Huff man Godei we need to Order , from Arronge probolal? ties an order: Atcind ing Bescendrng to F =0:25 - 25 ५2- 0-33 E = 0.2) 0-33- B = 0.2) - PO-24-3 Po25. C = 0.17 → 0.17 = D.10 -o = 0. 06 Huffronede lode legt Digital data trasd 10 000 000 0I 00 0010 || 00

teseff ede 8:11 D: 001) F:01 E: 10 loret opton. the abouue Ps so, ) None tae codes aboue O M auesoge vode lergith baug Pt → prohakiuty f code i, 9= AiB 1.CIDL n8 Jergth of code 8. EIF- Log = PA PA + Pe ng t Pcnc t Po?D t =(0,10)(4) + (ox) (2) † @•17) (3) + o 4)4) + co-21) (2) † c0:25) (>) 2-49. "2.45 not in the giuen oplron so, () none of the aboue 9s correet auquel.

entrony of letterg -( PA log (rm) + C Pe dog (Ps) t +( R log (Pe))+ CPo log CPo)) † ( PE loge DE)) + ( P loy( p) --l o-10 log,co-10) + o-21 log, (o1) + o:1a log (017) + 0.06 log, (0.06) + 021 log, (0:1) + 025 19(0-25)] - - C-245] f głuen letter is H=2-45: > su option C) 2.u5 9s the comeetone.