Conversion between number system Data representation presentation 1 2 variant
Оценка 4.9

# Conversion between number system Data representation presentation 1 2 variant

Оценка 4.9
ppt
01.05.2020
Conversion between number system Data representation presentation 1 2 variant.ppt

## Conversion between number system

Conversion between number system

## Learning objectives: Assesment criteria:

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

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

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

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.

## Algorithm transfer numbers from binary number system to decimal 1

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

Translation of numbers from decimal
number systems

## Algorithm converting integer decimal to binary 1

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

Converting a decimal number to binary

## Translation of arbitrary numbers from decimal system

Translation of arbitrary numbers
from decimal system

## Algorithm convert arbitrary numbers from decimal to binary

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

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?