ICT for Grade 10
Thursday, August 11, 2016
Introduction
A sequence, in mathematics, is a string of objects, like numbers, that follow a particular pattern. The individual elements in a sequence are called terms. Some of the simplest sequences can be found in multiplication tables:
- 3, 6, 9, 12, 15, 18, 21, …
Pattern: “add 3 to the previous number to get the next number” - 0, 12, 24, 36, 48, 60, 72, …
Pattern: “add 12 to the previous number to get the next number”
Of course we can come up with much more complicated sequences:
- 10,–2 8,×2 16,–2 14,×2 28,–2 26,×2 52, …
Pattern: “alternatingly subtract 2 and multiply by 2 to get the next number” - 0,+2 2,+4 6,+6 12,+8 20,+10 30,+12 42, …
Pattern: “add increasing even numbers to get the next number”
Add the next three terms to each number pattern and explain how you calculated these terms:
1.1 2; 7; 12; 17; …
1.2 10; 8; 6; 4; …
1.3 ;... 2 `1 ; 3 4 3 ; ;2 2 4 1 1
1.4 1; 3; 9; 27; …
1.5 1; 1; 2; 3; 5; 8; 13; …
1.2 10; 8; 6; 4; …
1.3 ;... 2 `1 ; 3 4 3 ; ;2 2 4 1 1
1.4 1; 3; 9; 27; …
1.5 1; 1; 2; 3; 5; 8; 13; …
Video Lessons
Convert Decimal to Binary
Convert Decimal to Binary
The decimal (base ten) numeral system has ten
possible values (0,1,2,3,4,5,6,7,8, or 9) for each place-value. In contrast,
the binary (base two) numeral system has two possible values represented as 0
or 1 for each place-value.[1] Since the binary system is the
internal language of electronic computers, serious computer programmers should
understand how to convert from decimal to binary.
1
Set up the problem.
For this example, let's convert the decimal
number 15610 to binary. Write the decimal number as the
dividend inside an upside-down "long division" symbol. Write the base
of the destination system (in our case, "2" for binary) as the
divisor outside the curve of the division symbol.
·
This method is much easier to understand when
visualized on paper, and is much easier for beginners, as it relies only on
division by two.
·
To avoid confusion before and after conversion,
write the number of the base system that you are working with as a subscript of
each number. In this case, the decimal number will have a subscript of 10 and
the binary equivalent will have a subscript of 2.
2
Divide. Write
the integer answer (quotient) under the long division symbol, and write the
remainder (0 or 1) to the right of the dividend.[2]
·
Since we are dividing by 2, when the dividend is
even the binary remainder will be 0, and when the dividend is odd the binary
remainder will be 1.
·
3
·
Continue to divide until
you reach 0. Continue downwards, dividing each new
quotient by two and writing the remainders to the right of each dividend. Stop
when the quotient is 0.
4
Write out the new, binary number. Starting with the bottom remainder, read the sequence of
remainders upwards to the top. For this example, you should have 10011100. This
is the binary equivalent of the decimal number 156. Or, written with base
subscripts: 15610 = 100111002
·
This method can be modified to convert from
decimal to any base. The divisor is 2 because the desired
destination is base 2 (binary). If the desired destination is a different base,
replace the 2 in the method with the desired base. For example, if the desired
destination is base 9, replace the 2 with 9. The final result will then be in
the desired base
.
.
Game
http://forums.cisco.com/CertCom/game/binary_game_page.htm
Subscribe to:
Posts (Atom)
