number systems revision introductory lesson decimal | binary | hexadecimal 1
TRANSCRIPT
Number Systems
Revision Introductory Lesson
Decimal | Binary | Hexadecimal
1
2
Decimal System
In this topic …
Binary System
Hexadecimal System
Conversions
3
Conversions …
Binary Decimal Decimal Binary
Binary Hexadecimal
Hexadecimal Binary
Decimal Hexadecimal
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Decimal System• Ten fingers• Ten different numbers possible: • 0 1 2 3 4 5 6 7 8 9
• Base 10 e.g. 654210
5
6 5 4 2100 = 1x 2 = 2101 = 10 x 4 = 40102 = 100 x 5 = 500103 = 1000 x 6 = 6000 + 6542
… 104 103 102 101 100 … 10000 1000 100 10 1
thou
sand
s
hund
reds
tens
units
6 5 4 2Our Number System
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Binary System
• Switch
• Two possible values: 0 and 1
• Base 2 E.g. 011101012
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Binary System
… 27 26 25 24 23 22 21 20
… 128 64 32 16 8 4 2 1 0 1 1 1 0 1 0 1
MSB LSB
Most Significant Bit Least Significant BitThe bit position having
the greatest valueThe bit position having
the least value
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Binary to Decimal Conversion
Q: Convert 011101012 to decimal.
A: 2 14816
32
64
128 0 1101110
64 + 32 + 16 + 4 + 1 = 11710
Add together the corresponding values where there is a 1
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Decimal to Binary ConversionMethod 1 – Using Long Division
Q: Convert 1810 to binary:
A: 1829
r 0
242 r 1
r 0
22120
r 0r 1
1810 = 0100102
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Decimal to Binary ConversionMethod 2 – Using Weights
Q: Convert 17310 to binary.
A: 2 14816
32
64
128 0 1110101
173 –128 45
45 –32 13
13 – 8 5
5 – 4
1
1 – 1 0
2
Working:
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Any Questions?