Unit 11 – Maths for Computing
2. PRELIMINARY LESSONS
1
2. Preliminary Lessons
2.1 Numbers
2.2 Number Systems
2.3 Algebra
2
2.2 Number Systems
2.2.1 Introduction
✓ A Number System is more or
less like a scale for
representing numerical
values.
✓ Different number systems
such as Decimal, Binary, Octal,
Duodecimal and Hexadecimal
are used by people.
3
2.2 Number Systems
2.2.1 Introduction
• A number system has a Base or a Radix
• There are several symbols used as digits.
• Number of symbols in the number system is equal to the value
of the base.
• The value of each digit is determined by
▪ the symbol used
▪ the position where it appears (Positional value)
4
2.2 Number Systems
2.2.1 Introduction
5
2.2 Number Systems
2.2.1 Introduction
Decimal Number System
6
2.2 Number Systems
2.2.2 Binary Number System
▪ Base 2 - (0-1)
▪ E.g.
❑101110012
❑1011.11012
7
2.2 Number Systems
2.2.2 Binary Number System
▪ Decimal to Binary & Binary to Decimal
E.g. Convert 25 into binary
8
2.2 Number Systems
2.2.2 Binary Number System
▪ Decimal to Binary & Binary to Decimal
E.g. Convert 0.65 into binary
9
2.2 Number Systems
2.2.2 Binary Number System
▪ Decimal to Binary & Binary to Decimal
E.g. Convert 1001012 into decimal
10
2.2 Number Systems
2.2.2 Binary Number System
▪ Decimal to Binary & Binary to Decimal
E.g. Convert 0.10112 into decimal
11
2.2 Number Systems
2.2.3 Octal Number System
▪ Base 8
(0-7)
▪ E.g.
❑235678
❑135.478
12
2.2 Number Systems
2.2.3 Octal Number System
▪ Decimal to Octal & Octal to Decimal
E.g. Convert 214 into octal
13
2.2 Number Systems
2.2.3 Octal Number System
▪ Decimal to Octal & Octal to Decimal
E.g. Convert 0.153 into octal
14
2.2 Number Systems
2.2.3 Octal Number System
▪ Decimal to Octal & Octal to Decimal
E.g. Convert 712638 into decimal
15
2.2 Number Systems
2.2.4 Duodecimal Number System
▪ Base 12
(0-9, A,B)
▪ E.g.
❑4020A12
❑102B.1112
16
2.2 Number Systems
2.2.4 Duodecimal Number System
▪ Decimal to Duodecimal & Duodecimal to Decimal
E.g. Convert 83242 into duodecimal
17
2.2 Number Systems
2.2.4 Duodecimal Number System
▪ Decimal to Duodecimal & Duodecimal to Decimal
E.g. Convert 4020A12 into decimal
18
2.2 Number Systems
2.2.5 Hexadecimal Number System
▪ Base 16 - (0-9 , A-F)
▪ E.g.
❑69AF16
❑457.2F16
19
2.2 Number Systems
2.2.5 Hexadecimal Number System
▪ Decimal to Hexadecimal & Hexadecimal to Decimal
E.g. Convert 765.24510 into hexadecimal
20
2.2 Number Systems
2.2.5 Hexadecimal Number System
▪ Decimal to Hexadecimal & Hexadecimal to Decimal
E.g. Convert A65.C216 into decimal
21
Summary
2. Preliminary Lessons
2.2 Number Systems
2.2.1 Introduction
2.2.2 Binary Number System
2.2.3 Octal Number System
2.2.4 Duodecimal Number System
2.2.5 Hexadecimal Number System
22
END OF THE SESSION
23