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Summary Topic II: Revision For Basic Mathematics
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  • Course
  • CSC1031 (CSC1031)
  • Institution
  • Newcastle University (NCL)

Cheat Sheet for Topic 2 in CSC1031 module, covering the basic mathematics such as *Conversions of binary to octal and hex. *Floating Point *Binary Addition and Multiplication * Highest and Lowest Common Factor *Fractions(Addition, Multiplication, Division)

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  • February 15, 2024
  • 4
  • 2023/2024
  • Summary

Subjects

  • csc1031
  • newcastle uni
  • maths
  • computer science
  • topic ii revision for basic mathematics

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  • Newcastle University (NCL)
  • Unknown
  • CSC1031 (CSC1031)
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CSC1031 – Semester 2 Examina3on




Fundamentals Of Computing


Topic II : Revision of Basic Mathematics


Representation of Numbers

- Base - 2 (binary): 0 and 1.

- Base - 8 (octal): 0 … 7.

- Base – 16 (Hexadecimal): 0 … 9 , A …F.




Binary Representation of Numbers

- Weights of position are power of 2:

1 = 20 , 2 = 21 , 4 = 20 8=23, 16=24

- In order to calculate the value of a number we multiple each digit by its weight as the following:

110012 =1(24) +1(23)+0(22)+0(21)+1(20)

= 16 + 8 + 1 = 2510

Fraction

- Decimal Fractions: 325.45 = 3*100 + 2*10 + 5*1 + 4*0.1 + 5*0.01

= 3*102 + 2*101 + 5*100 + 4*10-1 + 5*10-2

- Binary Fraction: 1101.1012 = 1*23 + 1*22 + 0*21 + 1*20 + 1*2-1 + 0*2-2 + 1*2-3

= 1*8 + 1*4 + 0*2 + 1*1 + 1*1/2 + 0*1/4 + 1*1/8 = 13.62510




Conversion to decimal

Base 8 – Octal: 7048 = 4*80 + 0*81 + 7*82 = 4*1 + 0*8 +7*64 = 45210

Base 16 – Hexadecimal: 3C216 = 2*160 + 12*161 + 3*162 = 2*1 + 12*16 + 3*256 = 96210




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