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CS101 Assignment 1 Solution Fall 2018

Objective:

  • To understand Number System
  • Number System conversion
  • To develop a truth table for logic operation.

Note:

It should be clear that your assignment will not get any credit (zero marks) if:
  • The assignment is submitted after the due date.
  • The submitted assignment is other than .doc or .docx file.
  • The submitted assignment does NOT open or file is corrupted.
  • Please avoid submitting copied assignments; otherwise, such a case would be referred to the discipline committee.
  • The font color should be preferably black and font size 12 Times New Roman.

Questions:  Marks: 20

Question #1:
Convert the following decimal numbers into equivalent binary numbers and then convert the binary answer back into equivalent decimal. Show all the steps of conversions:  3242
Sol:
I – Decimal to Binary Numbers: 3242
2 3242 Remainder
2 1621 0
2 810 1
2 405 0
2 202 1
2 101 0
2 50 1
2 25 0
2 12 1
2 6 0
2 3 0
1 1

Remainders from Bottom to top: (110010101010)2

II – Binary to Decimal Numbers: (110010101010)2

(110010101010)2 = 1×211 + 1×210 + 0x29 + 0x28 + 1×27 + 0x26 + 1×25 + 0x24 + 1×23 + 0x22 + 1×21 + 0x20

= 1×2048 + 1×1024 + 0x512 + 0x256 + 1×128 + 0x64 + 1×32 + 0x16 + 1×8 + 0x4 + 1×2 + 0x2

= 2048 + 1024 + 0 + 0 + 128 + 0 + 32 + 0 + 8 + 0 + 2 + 0

(110010101010)2= (3242)10

Question #2:
Solve the given Boolean Expression by using truth table. (AÅB) . ((A/ + C/) Å (A/+B))
Sol:
A B C AÅB A/ C/
(A/
+ C/)
(A/+B) (A/ + C/) Å (A/+B)
(AÅB).((A/ + C/)
Å (A/+B))
0 0 0 0 1 1 1 1 0 0
0 0 1 0 1 0 1 1 0 0
0 1 0 1 1 1 1 1 0 0
0 1 1 1 1 0 1 1 0 0
1 0 0 1 0 1 1 0 1 0
1 0 1 1 0 0 0 0 0 0
1 1 0 0 0 1 1 1 0 0
1 1 1 0 0 0 0 1 1 1
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