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ECE171

Winter2011

Homework1Solutions

1. [5]Usethesubtracttheweightsorrepeatedradixdivisionmethodtoconverteachofthefollowingdecimalintegerstobinary.a) 13b) 35c) 47d) 74e) 165

a) 1101b) 100011c) 101111d) 1001010e) 10100101

2. [5]Converteachofthefollowingbinarynumberstoitsequivalenthexadecimalrepresentationusingthegroupsof4method.

a) 10000101b) 10010110c) 10110111d) 11011100e) 11111011

a) 85b) 96c) B7d) DCe) FB

3. [5]Converteachofthefollowinghexadecimalnumberstoitsequivalentbinaryrepresentationusingthegroupsof4methodinreverse.

a) Db) 1Ac) 16d) 321e) BEAD

a) 1101b) 00011010c) 00010110d) 001100100001e) 1011111010101101

4. [10]Converteachofthefollowingbinarynumberstoitsequivalentoctalandhexadecimalrepresentations.

a) 10000001b) 101010100c) 10001000.111d) 1100001.1e) 110111.01

a) 8116=2018b) 15416=5248c) 88.E16=210.78d) 61.816=141.48e) 37.416=67.28

5.[5]Converteachofthefollowinghexadecimalnumberstoitsdecimalequivalentusingthepolynomialfunctionmethod.

a) 1516b) B216c) 10D16d) EE16e) 7C16

a) 2110b) 17810c) 26910d) 23810e) 12410

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6. [5]Fillinthetablebelow Decimal Binary Octal Hexadecimal20 1 1 1 1

21 2 10 2 2

22 4 100 4 423 8 1000 10 8

24 16 10000 20 10

25 32 100000 40 20

26 64 1000000 100 40

27 128 10000000 200 80

28 256 100000000 400 100

29 512 1000000000 1000 200

210 1024 10000000000 2000 400

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7. [5]Constructatableshowingthehexadecimalnumbersbetween00and20andtheircorrespondingbinaryequivalents.

Hexadecimal Binary

00 00000000

01 00000001

02 00000010

03 00000011

04 0000010005 0000010106 0000011007 0000011108 0000100009 000010010A 000010100B 000010110C 000011000D 000011010E 000011100F 0000111110 00010000

11 0001000112 0001001013 0001001114 0001010015 0001010116 0001011017 0001011118 0001100019 000110011A 000110101B 000110111C 000111001D 000111011E 000111101F 0001111120 00100000

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8. [6]Convertthedecimalnumber0.625toitsbinary,octal,andhexadecimalequivalents.

0.62510=0.1012=0.58=0.A16

9. [6]Convertthedecimalnumber13.9toitsbinary,octal,andhexadecimalequivalents.

13.910=1101.1110011002=15.714638=D.E616

Note:Theunderscoredfractionalportionofthebinaryequivalentrepeats.Becausetheoriginal

decimalnumberisgiventoasingledecimalofprecision,oronepartin10,weonlyrequirethe

sameofthebinarynumber,oronepartinabout16(about4bits).

Acceptableanswersforoctalandhexadecimaldependuponthenumberofbinarybitsyoure

consideringandwhetheryouconsideredtherepeatingpattern.