1. Positional notation is used to represent numbers in different number systems such as binary, octal, decimal, and hexadecimal. Each system uses a different set of digits ranging from 0-1 in binary to 0-9 and A-F in hexadecimal. 2. The value of each digit depends on its position, with the rightmost digit being the least significant bit or digit. More significant digits have greater weights that are powers of the radix or base of the system. 3. Converting a number between systems involves determining the place value of each digit based on its position, and then summing the values of each digit multiplied by its weight to obtain the number in the target system.

1. 1
ก ก ก ก ก
ก !" ก Positional Notation
ก ,- . / -ก - 0 (Absolute Value) 89ก: ,- ก
; กก ก ก<
!" กก ; -, ,ก :/
1. ; ก ::ก ; = ; > -, .
2 0,1 ; >: 0 C" 9
2. ; 10 / ::ก ;
3. ก = ; ก 9 -, = กE F E กGE.
กE A . 10
กE B . 11
กE C . 12
กE D . 13
กE E . 14
กE F . 15

2. ,:: ; =ก > P 0. ; 2 / - C" ; 16 !" , ,::
; = 2.1
,::- = S ,ก :
,:: ; > (Binary Number System) ,ก : 0. ,1
,:: ; . (Octal Number System) ,ก : 0-7
,:: ; >: (Decimal Number System) ,ก : 0-9
,:: ; >: ก (Hexadecimal Number System) ,ก : 0-9. ,
A-F
,:: ; ,> ก: S ก >_ ; 2 (Binary) --,
ก / ก ,.>/``a / ก ,.>/``a !" กb >C , ก >F . bก . ,ก
:>F . bก !" ,> ก: _ ก 9S bก ก>S _ก=

3. ก- ก _c ก . F S-, - .ก Bit . , Byte
Bit - bก >_ 0 1 0 !" > C. กE9, 8
S ; > /
Byte Character ก _ Bit ก 8 / >. ก ,-
1 f S ,ก : Bit 0 -, "0 8ก:= > = !" ก -,. ก , g
; > -" :ก ก - - ก = ; 2 C" 8 ก 0 -" ก .
; >: ก . ; >: _E S - . -" ก ,:: ;
. - ก ; >: _E S = ; 2 = ก S
ก :
กก : ก Weight ก 1 "กก # " $
: % & (11011101)2 + , - .
(11011101)2 = (1X27) + (1X26) + (0X25) + (1X24) + (1X23)+ (1X22) +
(0X21) + (1X20)
= 128 + 64 + 0 + 16 + 8 + 4 + 0 + 1
= (221)10
:% $ (1011.101)2 - .
1 0 1 1 . 1 0 1 9 :;<
2-3 0.125
2-2 0.0
2-1 0.5
-
20 1.
21 2.
22 0.
23 8.
(11.625)10
∴ (1011.101)2 = (11.625)10

4. ก
กก
1. + , > - . " ?& @ > 2 A#, BC A %@ $.> D
, $ .# (LSB)
2. > 9 :;< A#,% ก , 1 ? #,"$ 2 ก BC %#%@ H#A
- .
3. > , 2 A $I % A#,9 :;< BJ $< BC A#,%@ - .
$.> D ก .# (MSB)
:% $ (221)10 - .
2 221 BC 1 (LSB)
2 110 BC 0
2 55 BC 1
2 27 BC 1
2 13 BC 1
2 6 BC 0
2 3 BC 1
2 1 BC 1 (MSB)
0
∴ (221)10 = (11011101)2
"; #L#$+M, ?> ก (Weight) & @
% $ (221)10 = (NN)2
1. > ?> ก (Weight) ? L#$ Weight ก .# , A ก %> " %@
$ # ?
128 128 64 32 16 8 4 2 1
2. ก Weight ก .# & @ Weight " I > " ก & ,"+ ,A#,
ก %> " , ก
Weight 128 64 32 16 8 4 2 1

5. ก 128 + 64 + 0 + 16 + 8 + 4 + 0 + 1 = 221
- . 1 1 0 1 1 1 0 1
∴ (221)10 = (11011101)2
ก $ - . %# B $ - .
กก
1. 1. + , $ %> " O , %# B $ #,"$"; ก " & ,"
2. 2. + , > %# B $ ? & ," JP#,"$ 2 9 JP , $ก" 1 %@A#,
- . 0 & H, 9 JP กก" 1 ก 1 %@A#, - .
1
3. 3. + , > %# B $ A#,% ก9 ก JP+ ? & @ JP#,"$ 2 & @:% P
9 :;< M #$"ก , & @ก @ " ก ?%@ > A $ I % ก" 9 JP%@
ก 1 A#, & $> :$ : & ,"
: % $ (0.375)10 - .
9 ก JP 9 %> " O
0.375 X 2 = 0.75 0
0.75 X 2 = 1.5 1
0.5 X 2 = 1.0 1
# ? (0.375)10 = (0.011)2

6. : % $ (12.35)10 - .
1. 1. $ (12)10 + , - .
(12)10 = (1100)2
2. $ (0.35)10 - .
9 ก JP 9 %> " O
0.35 X 2 = 0.7 0
0.7 X 2 = 1.4 1
0.4 X 2 = 0.8 0
0.8 X 2 = 1.6 1
0.6 X 2 = 1.2 1
0.2 X 2 = 0.4 0
0.4 X 2 = 0.8 0
0.8 X 2 = 1.6 1
ก $ %@Q?> ก A $ I %@ > +M, :$ 6
# ? (12.35)10 = (1100.010110)2