Questions
14:332:231:01 DIGITAL LOGIC DESIGN 04B Numbers and Base Conversion
Multiple fill-in-the-blank
Convert each of the following octal digits to 3 binary digits to create the fractions (26.2)8 = [Fill in the blank] (222)8 = [Fill in the blank] (364)8 = [Fill in the blank]
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Step-by-Step Analysis
First, I will restate the task and list the candidate answers given. The problem asks to convert each octal digit to three binary digits to form binary representations for the numbers: (26.2)8, (222)8, and (364)8. The provided answer options are:
- 10110.01
- 010110.010
- 010010010
- 10010010
- 11110100
- 011110100
Now I will evaluate each option in turn.
Option 1: 10110.01
- Why this is incorrect for (26.2)8: In octal-to-binary conversion, each octal digit becomes exactly three binary digits. The digits 2 and 6 convert to 010 and 110 respectively, so the integer part should be 010110, not 10110 (which is missing a leading zero and would be misinterpreted). The fractional part .2 should become .010, not .01. Overall, 10110.01 fails the required three-bits-per-octal-digit rule and omits the necessary leading zero.
Option 2: 010110.010
- Why this is correct for (26.2)8: Digits: 2......Login to view full explanationLog in for full answers
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Question textCharacter encodings Complete the questions below based on the following encoding table. The table contains 128 different characters, numbered from 0 to 127. Note how the characters of the English alphabet are not listed in the usual order. However, the order of lower-case and upper-case characters is the same: The table lists the lower-case characters first (starting with n, w, f, ...), followed by some symbols and then the upper-case characters (N, W, F, ...). For each character, you are given its hexadecimal code. For example, the character ] has hex code 2a. ! 00 j 20 Y 40 … 60 @ 01 * 21 M 41 æ 61 # 02 ( 22 T 42 “ 62 $ 03 ) 23 H 43 ‘ 63 % 04 - 24 B 44 « 64 ^ 05 + 25 G 45 » 65 & 06 = 26 O 46 ™ 66 n 07 { 27 S 47 £ 67 w 08 } 28 L 48 ¢ 68 f 09 [ 29 C 49 € 69 i 0a ] 2a K 4a ∞ 6a x 0b ∫ 2b A 4b § 6b r 0c \ 2c V 4c ¶ 6c q 0d : 2d E 4d • 6d y 0e 0 2e U 4e ª 6e m 0f 1 2f P 4f º 6f t 10 2 30 D 50 ≠ 70 h 11 3 31 Z 51 ± 71 b 12 4 32 J 52 ‡ 72 g 13 5 33 ; 53 | 73 o 14 6 34 " 54 74 s 15 7 35 < 55 ¯ 75 l 16 8 36 > 56 ˘ 76 c 17 9 37 , 57 ¿ 77 k 18 0 38 . 58 Ú 78 a 19 N 39 / 59 Æ 79 v 1a W 3a ? 5a µ 7a e 1b F 3b ` 5b © 7b u 1c I 3c ~ 5c ® 7c p 1d X 3d ≤ 5d ¬ 7d d 1e R 3e ≥ 5e √ 7e z 1f Q 3f ÷ 5f ≈ 7f Encoding and number systems Convert the letters of the word "Lion" into the corresponding character codes from the table above. The final letter has already been converted for you. You can look up the hexadecimal code in the table. Then convert the code into the different number representations (decimal, binary) by hand. Enter each number without leading zeros, and without type indicators such as 0x or 0b. [table] Character | Hex | Decimal | Binary L | Answer 1 Question 2 | Answer 2 Question 2 | Answer 3 Question 2 i | Answer 4 Question 2 | Answer 5 Question 2 | Answer 6 Question 2 o | Answer 7 Question 2 | Answer 8 Question 2 | Answer 9 Question 2 n | 07 | 7 | 111 [/table] Decoding Decode the following 4-letter word. Each character is given in binary notation. Convert the binary to hexadecimal and then look up the character in the encoding table above. [table] Binary | Hex | Character 111010 | Answer 10 Question 2 | Answer 11 Question 2 10100 | Answer 12 Question 2 | Answer 13 Question 2 10110 | Answer 14 Question 2 | Answer 15 Question 2 1001 | Answer 16 Question 2 | Answer 17 Question 2 [/table]
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