cs-3333: add hw3
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361
Fall-2024/CS-3333/Assignments/3/HW3.typ
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361
Fall-2024/CS-3333/Assignments/3/HW3.typ
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@ -0,0 +1,361 @@
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#set page(margin: (x: .5in, y: .5in))
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#let solvein(solution) = {
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let outset = 3pt
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h(outset)
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box(
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outset: outset,
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stroke: blue + .3pt,
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fill: rgb(0, 149, 255, 15%),
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radius: 4pt,
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)[#solution]
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}
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#let solve(content) = [
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#align(
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center,
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block(
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inset: 5pt,
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stroke: blue + .3pt,
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fill: rgb(0, 149, 255, 15%),
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radius: 4pt,
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)[#align(left)[#content]],
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)
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]
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#let notein(content) = {
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let outset = 3pt
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h(outset)
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box(
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outset: outset,
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stroke: luma(20%) + .3pt,
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fill: luma(95%),
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radius: 4pt,
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)[#content]
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}
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#let note(content) = [
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#align(
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center,
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block(
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inset: 5pt,
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stroke: luma(20%) + .3pt,
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fill: luma(95%),
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radius: 4pt,
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)[#align(left)[#content]],
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)
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]
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#align(center)[
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= CS 3333 Mathematical Foundations
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Homework 3 (100 points)\
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#underline[Price Hiller] *|* #underline[zfp106]
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]
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#line(length: 100%, stroke: .25pt)
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= Submission:
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Same as HW1.
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= Questions
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Convert a number in a number system to another one. *Write down the intermediate steps of your calculations.*
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+ Decimal numbers to binary numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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$157$
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#notein[
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$
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(157)_10 &= 2 ⋅ 78 &+ #text(red)[1]\
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78 &= 2 ⋅ 39 &+ #text(red)[0]\
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39 &= 2 ⋅ 19 &+ #text(red)[1]\
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19 &= 2 ⋅ 9 &+ #text(red)[1]\
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9 &= 2 ⋅ 4 &+ #text(red)[1]\
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4 &= 2 ⋅ 2 &+ #text(red)[0]\
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2 &= 2 ⋅ 1 &+ #text(red)[0]\
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1 &= 2 ⋅ 0 &+ #text(red)[1]
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$
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#solve[$(157)_10 = (10011101)_2$]
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]
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],
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[
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$39.25$
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#notein[
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#align(center)[#underline[Whole Number]]
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$
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(39)_10 &= 2 ⋅ 19 &+ #text(red)[1]\
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19 &= 2 ⋅ 9 &+ #text(red)[1]\
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9 &= 2 ⋅ 4 &+ #text(red)[1]\
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4 &= 2 ⋅ 2 &+ #text(red)[0]\
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2 &= 2 ⋅ 1 &+ #text(red)[0]\
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1 &= 2 ⋅ 0 &+ #text(red)[1]
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$
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#align(center)[#underline[Fraction]]
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$
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.50 &= 0.25 ⋅ 2 #note[#text(red)[0]]\
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1.00 &= 0.50 ⋅ 2 #note[#text(red)[1]]
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$
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#solve[$(39.25)_10 = (100111.01)_2$]
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]
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],
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)
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+ Binary numbers to decimal numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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$(10111010)_2$
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#notein[
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$
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(1 ⋅ 2^7) + (0 ⋅ 2^6) + (1 ⋅ 2^5) + (1 ⋅ 2^4) + (1 ⋅ 2^3) + (0 ⋅ 2^2) + (1 ⋅ 2^1) + (0 ⋅ 2^0) = #solve[$(186)_10$]
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$
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]
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],
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[
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$(1101.011)_2$
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#notein[
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$
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(1 ⋅ 2^3) + (1 ⋅ 2^2) + (0 ⋅ 2^1) + (1 ⋅ 2^0) + (0 ⋅ 2^-1) + ( 1 ⋅ 2^-2) + (1 ⋅ 2^-3) = #solve[$(13.375)_10$]
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$
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]
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],
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)
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+ Octal integers to binary numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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$(527)_8$
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#notein[
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#table(
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columns: (auto, auto, auto, auto),
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[*Octal*], [$5$], [$2$], [$7$],
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[*Binary*], [$101$], [$010$], [$111$],
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)
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#solve[$(527)_8 = (101010111)_2$]
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]
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],
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[
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$(4361)_8$
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#notein[
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#table(
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columns: (auto, auto, auto, auto, auto),
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[*Octal*], [$4$], [$3$], [$6$], [$1$],
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[*Binary*], [$100$], [$011$], [$110$], [$001$],
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)
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#solve[$(4361)_8 = (100011110001)_2$]
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]
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],
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)
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+ Octal integers to decimal numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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$(527)_8$
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#notein[
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$
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(5 ⋅ 8^2) + (2 ⋅ 8^1) + (7 ⋅ 8^0) = #solve[$(343)_10$]
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$
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]
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],
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[
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$(4361)_8$
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#notein[
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$
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(4 ⋅ 8^3) + (3 ⋅ 8^2) + (6 ⋅ 8^1) + (1 ⋅ 8^0) = #solve[$(2289)_10$]
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$
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]
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],
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)
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+ Binary numbers to octal numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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$(10 110 110)_2$
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#notein[
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#table(
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columns: (auto, auto, auto, auto),
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[*Binary*], [$#text(red)[0]10$], [$110$], [$110$],
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[*Octal*], [$2$], [$6$], [$6$],
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)
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#solve[$(10 110 110)_2 = (266)_8$]
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]
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],
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[
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$(11 110.011)_2$
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#notein[
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#table(
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columns: (auto, auto, auto, auto),
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[*Binary*], [$#text(red)[0]11$], [$110$], [$011$],
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[*Octal*], [$3$], [$6$], [$3$],
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)
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#solve[$(11 110.011)_2 = (36.3)_8$]
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]
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],
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)
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+ Hexadecimal integers to binary numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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(F$6$A$)_16$
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#notein[
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#table(
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columns: (auto, auto, auto, auto),
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[*Hexadecimal*], [F], [$6$], [A],
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[*Binary*], [$1111$], [$0110$], [$1010$],
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)
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#solve[(F6A$)_16 = (1111 0110 1010)_2$]
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]
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],
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[
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(D$0$EB$)_16$
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#notein[
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#table(
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columns: (auto, auto, auto, auto, auto),
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[*Hexadecimal*], [D], [$0$], [E], [B],
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[*Binary*], [$1101$], [$0000$], [$1110$], [$1011$],
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)
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#solve[(D$0$EB$)_16 = (1101 0000 1110 1011)_2$]
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]
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],
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)
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+ Hexadecimal integers to decimal numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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(F6A$)_16$
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#notein[
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$
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(15 ⋅ 16^2) + (6 ⋅ 16^1) + (10 ⋅ 16^0) = #solve[$(3946)_10$]
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$
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]
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],
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[
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(D0EB$)_16$
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#notein[
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$
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(13 ⋅ 16^3) + (0 ⋅ 16^2) + (14 ⋅ 16^1) + (11 ⋅ 16^0) = #solve[$(53483)_10$]
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$
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]
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],
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)
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+ Binary numbers to hexadecimal numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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$(10 1101. 011)_2$
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#notein[
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#table(
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columns: (auto, auto, auto, auto),
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[*Binary*], [$#text(red)[00]10$], [$1101$], [$011#text(red)[0]$],
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[*Hexadecimal*], [$2$], [D], [$6$],
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)
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#solve[$(10 1101. 011)_2 = (2$D$.6)_16$]
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]
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],
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[
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$(1 1011 1101)_2$
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#notein[
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#table(
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columns: (auto, auto, auto, auto),
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[*Binary*], [$#text(red)[000]1$], [$1011$], [$1101$],
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[*Hexadecimal*], [$1$], [B], [D],
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)
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#solve[$(1 1011 1101)_2 = (1$BD$)_16$]
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]
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],
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)
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+ Octal numbers to hexadecimal numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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$(605.35)_8$
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#notein[
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1. #underline[Octal to Binary]
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#table(
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columns: (auto, auto, auto, auto, auto, auto, auto),
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[*Octal*], [$6$], [$0$], [$5$], [$.$], [$3$], [$5$],
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[*Binary*], [$110$], [$000$], [$101$], [$.$], [$011$], [$101$],
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)
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#note[$=11 000 0101 .011 101$]
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//$=1 1000 0101.0111 01$
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2. #underline[Binary to Hexadecimal]
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#table(
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columns: (auto, auto, auto, auto, auto, auto, auto),
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[*Binary*],
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[$#text(red)[000]1$],
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[$1000$],
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[$0101$],
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[$.$],
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[$0111$],
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[$01#text(red)[00]$],
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[*Hexadecimal*], [$1$], [$8$], [$5$], [$.$], [$7$], [$4$],
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)
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#solve[$(605.35)_8 = (185.74)_16$]
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]
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],
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)
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+ Hexadecimal numbers to octal numbers. (10 pts)
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#enum(
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numbering: "a.",
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[
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(C$9$A.$3$B$)_16$
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#notein[
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1. #underline[Hexadecimal to Binary]
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#table(
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columns: (auto, auto, auto, auto, auto, auto, auto),
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[*Hexadecimal*], [C], [$9$], [A], [$.$], [$3$], [B],
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[*Binary*], [$1100$], [$1001$], [$1010$], [$.$], [$0011$], [$1011$],
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)
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#note[$=1100 1001 1010 . 0011 1011$]
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//$=110 010 011 010.001 110 11
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2. #underline[Binary to Octal]
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#table(
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columns: (auto, auto, auto, auto, auto, auto, auto, auto, auto),
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[*Binary*],
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[$110$],
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[$010$],
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[$011$],
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[$010$],
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[$.$],
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[$001$],
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[$110$],
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[$11#text(red)[0]$],
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[*Octal*], [$6$], [$2$], [$3$], [$2$], [$.$], [$1$], [$6$], [$6$],
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)
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#solve[(C$9$A.$3$B$)_16 = (6232.166)_8$]
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]
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],
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)
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