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Презентация на тему Arithmetic fundamentals of number systems

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2. OutlineDifferent number systemsWhy use different ones?Binary / Octal / HexadecimalConversionsNegative number representationBinary arithmeticOverflow / Underflow
3. Number SystemsFour number systems:Decimal (10)Binary (2)Octal (8)Hexadecimal (16)
4. Binary numbersComputers work only on two statesOnOffBasic
5. Decimal numbers1439 = 1 x 103 +
6. Binary Decimal1101 = 1
7. Decimal Binary13631022221011(13)10 = (1101)2MSBLSB
8. Octal Decimal 137 =
9. Decimal Octal951110888731(95)10 = (137)8MSPLSP
10. Hex DecimalBAD = 11 x
11. Decimal Hex 298918611016 1616131011(2989)10 = (BAD)16MSPLSP
12. Why octal or hex?Ease of use and
13. Roman Numerals
14. A Brief History of Roman Numerals Roman
15. Arabic numbers → Roman numerals conversionRoman numerals
16. As a general guideRoman Numerals are made
17. VIII = 5+3 = 8XIX = 10+
18. Check your answers.7 = VII12 = XII15 = XV20 = XX
19. Can you convert these numbers to Roman
20. Were you correct?17=XVII 22=XXII 26=XXVI 29=XXIX
21. Some more large numbers to try:600 =
22. Check your answers.600 = DC 700
23. The last oneCan you convert 2017?MMXVIINow try
24. Binary ArithmeticAdditionSubtraction
25. AdditionLike normal decimal addition
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27. Похожие презентации

OutlineDifferent number systemsWhy use different ones?Binary / Octal / HexadecimalConversionsNegative number representationBinary arithmeticOverflow / Underflow

Arithmetic fundamentals of number systemsSabina BatyrkhanovnaPhD, assistant professor

Number SystemsFour number systems:Decimal (10)Binary (2)Octal (8)Hexadecimal (16)

Binary numbersComputers work only on two statesOnOffBasic memory elements hold only two

Decimal numbers1439 = 1 x 103 + 4 x 102 + 3

Decimal Binary13631022221011(13)10 = (1101)2MSBLSB

Decimal Octal951110888731(95)10 = (137)8MSPLSP

Decimal Hex 298918611016 1616131011(2989)10 = (BAD)16MSPLSP

Why octal or hex?Ease of use and conversionThree bits make one octal

A Brief History of Roman Numerals Roman numerals originated in ancient Rome.

Arabic numbers → Roman numerals conversionRoman numerals are written as combinations of

As a general guideRoman Numerals are made up by adding or subtracting

VIII = 5+3 = 8XIX = 10+ 9 = 19 (Remember 9

Check your answers.7 = VII12 = XII15 = XV20 = XX

Can you convert these numbers to Roman Numerals? 17 =

Were you correct?17=XVII 22=XXII 26=XXVI 29=XXIX 30=XXX 32=XXXII

Some more large numbers to try:600 = 700 =

Check your answers.600 = DC 700 = DCC 800

The last oneCan you convert 2017?MMXVIINow try to write today’s date.

SubtractionLike normal decimal subtraction

Слайды презентации

Слайд 2 Outline
Different number systems
Why use different ones?
Binary / Octal

/ Hexadecimal
Conversions
Negative number representation
Binary arithmetic
Overflow / Underflow

Слайд 3 Number Systems
Four number systems:
Decimal (10)
Binary (2)
Octal (8)
Hexadecimal (16)

Слайд 4 Binary numbers
Computers work only on two states
On
Off
Basic memory

Binary numbersComputers work only on two statesOnOffBasic memory elements hold only

elements hold only two states
Zero / One
Thus a number

system with two elements {0,1}
A binary digit – bit !

Слайд 5 Decimal numbers

1439 = 1 x 103 + 4

Decimal numbers1439 = 1 x 103 + 4 x 102 +

x 102 + 3 x 101 + 9 x

100

Thousands Hundreds Tens Ones

Radix = 10

Слайд 6 Binary Decimal
1101 = 1 x

23 + 1 x 22 + 0 x 21

+ 1 x 20
= 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1
= 8 + 4 + 0 + 1

(1101)2 = (13)10

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, …

Слайд 7 Decimal Binary
13
6
3
1
0
2
2
2
2
1
0
1
1
(13)10 = (1101)2

MSB
LSB

Слайд 8 Octal Decimal
137 = 1

x 82 + 3 x 81 + 7 x

80
= 1 x 64 + 3 x 8 + 7 x 1
= 64 + 24 + 7

(137)8 = (95)10

Digits used in Octal number system – 0 to 7

Слайд 9 Decimal Octal
95
11
1
0
8
8
8
7
3
1
(95)10 = (137)8

MSP
LSP

Слайд 10 Hex Decimal
BAD = 11 x 162

+ 10 x 161 + 13 x 160

= 11 x 256 + 10 x 16 + 13 x 1
= 2816 + 160 + 13

(BAD)16 = (2989)10

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Слайд 11 Decimal Hex
2989
186
11
0
16
16
16
13
10
11
(2989)10 = (BAD)16

MSP
LSP

Слайд 12 Why octal or hex?
Ease of use and conversion
Three

Why octal or hex?Ease of use and conversionThree bits make one

bits make one octal digit
111

010 110 101
7 2 6 5 => 7265 in octal

Four bits make one hexadecimal digit
1110 1011 0101
E B 5 => EB5 in hex

4 bits = nibble

Слайд 13 Roman Numerals

Слайд 14 A Brief History of Roman Numerals
Roman numerals

A Brief History of Roman Numerals Roman numerals originated in ancient

originated in ancient Rome. This ancient counting system is

believed to have started with the ancient Etruscans.
The symbol for one in the roman numeral system probably represented a single tally mark which people would notch into wood or dirt to keep track of items or events they were counting. It would also be easy to write on a wax tablet.

Слайд 15 Arabic numbers → Roman numerals conversion
Roman numerals are

Arabic numbers → Roman numerals conversionRoman numerals are written as combinations

written as combinations of seven letters.
I = 1

V = 5 X = 10 L = 50
C = 100 D =500 M = 1000
The letters can be written as capital (XVI) or lower-case letters (xvi).

Слайд 16 As a general guide
Roman Numerals are made up

As a general guideRoman Numerals are made up by adding or

by adding or subtracting numbers like this:-
11=10+1 =

XI 9 = 10 – 1 = IX
40 = 50 –10 = XL
If you want to say 1,100 in Roman Numerals, you would say M for 1000 and then put a C after it for 100; 1,100 = MC
900 =1000 – 100 so the C comes before M = CM