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Conversion between number system Data representation presentation 1 2 variant.ppt
Conversion between number system
Learning objectives:
Assesment criteria:
Translates numbers from decimal to binary
Translations of the number of one number system to another
Convert decimal numbers to binary numbers and vice versa
The number system is a sign system in which numbers are written according to certain rules using the symbols of a certain alphabet, called numbers.
Number systems
Non-positional
positional
In positional number systems, the quantitative value of a digit depends on its position in the number.
In nonpositional numeral systems, the quantitative value of a digit does not depend on its position in the number
5
7
9
5
7
9
XI (11) adding the number to the right of the number, add it
IX (9) appending the number to the left of the number, take it away.
I - one
X - ten
- hundreds
- tens
- units
Number systems
Non-positional
positional
1. Decimal СС
0..9
2. Binary CC
0, 1
3. Octal SS
0..7
4. Hex hex
0..9, A, B, C, D, E, F
In positional SS, the base of the system is equal to the number of digits (characters in its alphabet) and determines how many times the values of the same digits standing in adjacent positions differ
Roman СС
I - one
V - five
X - ten
L - fifty
C - one hundred
D - five hundred
M - one thousand
Egyptian СС
Greek СС
What are the number systems used for?
2. How are positional number systems different from non-positional?
3. What are the numbers in the alphabet of the decimal number system, binary, octal and hexadecimal?
Compare the numbers VVV and 555.
11012 = 1*23 +0*22 +1*21 +1*20 = = 8 + 2 + 1 = 1110
10,012 = 1*21 + 0*20 + 0*2-1 + +1*2-2 = 2 + 0,25 = 2,2510
Algorithm transfer numbers from binary number system to decimal
1. Write the binary number in expanded form
2. Make calculations
Translation of numbers from decimal
number systems
Algorithm
converting integer decimal to binary
1. To consistently divide the whole decimal number and the resulting partial quotients by the base of the system (by 2) until the quotient from the division is equal to zero;
2. Write the resulting residues in reverse order.
75 10 = 10010112
75:2=37 ост.1
37:2=18 ост.1
18:2=9 ост.0
9:2=4 ост.1
4:2 = 2 ост. 0
2:2 = 1 ост.0
1 : 2 = 0 ост.1
18010 = 101101002
180 :2 = 90 ост.0
90 : 2 = 45 ост.0
45 : 2 = 22 ост.1
22 : 2 = 11 ост.0
11 : 2 = 5 ост.1
5 : 2 = 2 ост.1
2 : 2 = 1 ост.0
1 : 2 = 0 ост.1
Converting a decimal number to binary
Translation of arbitrary numbers
from decimal system
40,510 = 101000,12
0, 5
* 2
0
40 : 2 = 20 ост. 0
20 : 2 = 10 ост.0
10 : 2 = 5 ост. 0
5 : 2 = 2 ост.1
2 : 2 = 1 ост.0
1 : 2 = 0 ост.1
Algorithm convert arbitrary numbers from decimal to binary
Convert the integer part of the number to the binary number system
Convert the fractional part of the number to the binary number system according to the appropriate algorithm.
In the final record of the resulting number, the integer part is separated from the fractional part by a comma.
In the class 11102 girls and 11002 boys. How many students are in a class?
What is the decimal equivalent of the numbers 101012, 11012?
I have 100 brothers. The youngest is 1000 years old, and the oldest is 1111 years old. Senior is in 1001 class. Could it be like that?
Additional task
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