Review-Questions-on-Digital-Number-Representation2

Review-Questions-on-Digital-Number-Representation2 - Review...

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Page 1 of 9 Revised 15 Sep 1998; corrected 19 Jan 2004 © 2004 Charles Abzug Review Questions: Digital Number Representation © 2004 Charles Abzug 1. What is the significance of the use of the word “digit” to represent a numerical quantity? 2. Which radices are “natural” (i.e., they correspond to some aspect of human anatomy)? What is their anatomical tie-in? 3. What is the principal advantage of the (Zoroastrian) sexagesimal (base 60) number system? 4. How long ago did the concept of zero originate? 5. (a) How many different numbers (or different anythings) can be represented by n bits? (b) How many different items are representable with 24 bits? 32? 48? (c) How could you rapidly determine how many different items are representable with any given number of bits that you might be asked about? 6. How should you go about converting a number from decimal representation to another radix? 7. Sample Problems: Convert each of the following decimal numbers to the radices indicated: (a) 2,346.1359 to radix 3, radix 9, and radix 16. (b) 7,924.9483 to radix 2, radix 5, and radix 11. (c) 1,781.1953 to radix 7, radix 8, and radix 13. 8. How should you go about converting from other radices to decimal? 9. Sample Problems: Convert each of the following numbers to decimal: (a) 111001010111.000101110111 2
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Review Questions: Digital Number Representation Page 2 of 9 Revised 15 Sep 1998; corrected 19 Jan 2004 © 2004 Charles Abzug (b) 123.321 4 (c) 123.4 7 (d) 7123.4567 8 (e) 123.4 9 (f) 123.4 11 (g) E56.D78 16 10. How should you interconvert among binary, octal, and hex? 11. Sample Problems: Each of the following numbers is written either in binary or in octal or in hexadecimal. Convert it to the other two radices. (a) 10101010101.0101010101 2 (b) 10111011101.1101110111 2 (c) 10101.0101 8 (d) 11101.11011 8 (e) 101.01 16 (f) 1101.11 16 (g) 12345.67124 8 (h) 12345.67124 16 (i) DEAD.ACE 16 (j) BAD.BEEF 16
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Review Questions: Digital Number Representation Page 3 of 9 Revised 15 Sep 1998; corrected 19 Jan 2004 © 2004 Charles Abzug Answers to Selected Questions: Question 2: Which radices are “natural” (i.e., they correspond to some aspect of human anatomy)? What is their anatomical tie-in? Radix Name of Scheme Anatomical Basis 5 Quinary Number of fingers on one hand 10 Decimal Number of fingers on both hands 12 Duodecimal Number of finger joints that can be pointed to from the thumb 20 Vigesimal Total number of fingers and toes together 24 Number of finger joints that can be pointed to from both thumbs Question 3: What is the principal advantage of the (Zoroastrian) sexagesimal (base 60) number
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Review-Questions-on-Digital-Number-Representation2 - Review...

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