Full summary, according to SAGS document, of IEB Information Technology Theory - Data Representation section. Includes detailed, step-by-step explanation of converting between number systems (binary, hexadecimal, decimal).
Information that facts have
processed data (in such meaning (
-> a
way
knowledge
+
familiarity with information gained
through experience
Computers only understand 1 electricity and O :
no
electricity
: all data must be represented as a series of O's and 1's
Decimal system
-
IC - ...
base 10 (digits ( -a)
102 10'100
18910910410310210'10 ex 106 , - 100 10 I
x
.
e 1888 1000100 10 I I o 6
I I I
/x100 OX10 1 x
6
Binary system
-
2 D :. base 2
(digits 0 and 1)
↳
bit-binary digit (011)
8 bits
byte
↳ =
>
*
2222222
2561286432168421
Hexadecimal
-
- system BE
10 :. base A-F)
16
(digits 0-9
+
, =12 F =
15
163
2
16 16'168
4096 256 16 I
~Table method (convert to decimal
converting between systems - Ladder method (convert from decimall
↳ Split +table/ladder binary c nexadecimal
Table method :
fill in
right -> left
↑ 8
3
16 ↑ 2 1
...
***
multiply
power r, -n
each
xo -base &... 256 16 I
column +
add
~ Du
3 a
digits of number cifletter, convert to
get number
3 to its digit
=(X ) (x xD) (x' D3) (x" Da)
↳ fill in
xD + +
+ + + left ->
right
. !
11010102 Xia
=
D1D0
eg) .
2
.
,6
256128643216842 1 4096 256 16 I
, 1 0 0 10 D13 I D'3 O
=
64 32 0 + + +
8 +
0 +
2 +
0 =
=(4096x3) +
(256 x
1) +
(16x13) (1x0) +
=106 ,0
=
53248 +
256 +
208
=53 TR ,0
Ladder method :
(number (basel ~ rein , I ·
Start With number , continuously divide by base write remainder
(base) reme only stop when you reach zero
(basel remainder bottom -> top= number
rem
·
(base)
rem
0 : number remeremz rem, rem
=
,
/
12 140 Xia
eg 1 140 - =
, c 2 .
, 0
.
14O Z ⑧ -
140
P
70 2 0 16 12 =
3
I
I 816 8
E 800
=
O
-100011002
⑧
, Split +table (binary -> hexadecimall
Split into hibbles bits)
·
(4
Use table method for each nibble to get hexadecimal value for each digit
·
941110111'
·
at number (binary (
+ I t
columns
-multiply
+ +
+
A
4
add letters
-
+
convert to if needsbe
D
number <Xiab
eg 111012 xix
=
8 4 2 I 8 42 I
I I I I 0 I I
n +
2 + I 8 +
0 +
2
+
1
Y B =
7Bix
Split + ladder chexadecimal
binary (
·
split hexadecimal number into individual digits (if letter-convert to number)
· do ladder for each
digit (if I
digits, put O's until it has h)
in order of
· read each ladder bottom-stop put together digits
+
DF,
eg Xc
=
D =
13 I =
15
a
13 2 In
S
,
62 O
3 3 2 i
i
2
12 2 I =11011111z
O !
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