Ele147

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Published on March 3, 2014

Author: waleedmahmoud1881975

Source: slideshare.net

 ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬١٤٧

 ‫٧٤١ א‬ ‫א‬  ‫א‬ ‫א‬     W،،‫א‬‫א‬،‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬  ،‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬        ،‫א‬ ‫א‬‫א‬   ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،   ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬      ‫א‬  ‫א‬   ،‫א‬     K‫א‬‫א‬،‫א‬‫א‬  ?    ?  ?  ‫א‬ ? ‫א‬ ‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬  K‫א‬ ‫א‬‫א‬‫א‬‫א‬       

 ‫٧٤١ א‬ ‫א‬  ‫א‬       ،KKK‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬      K‫א‬‫א‬،‫א‬،‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬،  ‫א‬،‫א‬‫א‬‫א‬‫א‬    K‫א‬‫א‬  KKKKKK،‫א‬ 

 ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬ ١

‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬‫א‬‫א‬   W‫א‬‫א‬ K‫א‬‫א‬‫א‬ • K‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬ • -١-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Introduction١J ١   ‫א‬   (Binary Number System)‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬  K(Digital Electronic Circuits) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬ K‫א‬(Decimal Number System)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K(Hexadecimal Numbering System)‫א‬‫א‬‫א‬(Octal Number System)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬K١  K‫א‬‫א‬‫א‬K٢  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K٣  K‫א‬‫א‬‫א‬‫א‬K٤  K‫א‬‫א‬‫א‬‫א‬‫א‬K٥ (Digit)‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬(Symbol)،(Number)‫א‬ ‫א‬‫א‬‫א‬(0,1,2,3,4, ... , 8,9)،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ،‫א‬(123)‫א‬‫א‬‫א‬(14)‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬(1,4)(14)‫א‬‫א‬‫א‬‫א‬  ‫א‬(6)(1,2,3)(123)  K‫א‬ -٢-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Decimal Numbering System‫א‬‫א‬‫א‬٢J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (10)‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬  (10)10‫א‬  K0,1,2,3,4,5,6,7,8,9  (128)‫א‬‫א‬(Positional Weight)‫א‬‫א‬ ،‫א‬ E‫א‬F‫א‬‫א‬(8)‫א‬‫א‬  ‫א‬(2)‫א‬‫א‬،(8 × 1 = 8) 1‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬  E‫א‬F‫א‬‫א‬E1F‫א‬‫א‬،(2 × 10 = 20)10  ‫א‬K(1 × 100 = 100) 100‫א‬‫א‬‫א‬  W،‫א‬‫א‬‫א‬‫א‬‫א‬  (1 × 100) + (2 × 10) + (8 × 1) = 100 + 20 + 8 = 128 ‫א‬‫א‬E10F‫א‬‫א‬‫א‬  W100 = 110 ‫א‬‫א‬‫א‬‫א‬  ........ 105 104 103 102 101 100  W128‫א‬ 1     (128)10 2 8  ‫א‬‫א‬‫א‬‫א‬ 102 1 × 102 = 100 101 100 + 2 × 101 + 8 × 100 + 20 + 8    ‫א‬10‫א‬‫א‬(128)‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬(Subscript)‫א‬ -٣-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W10-1‫א‬  102 101 100 • 10-1 10-2 10-3 ........  ‫א‬‫א‬ (Decimal Point)   Binary Numbering System‫א‬‫א‬‫א‬٣J ١  (2)(2) ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ .(1,0)‫א‬ ..... 2 4 ..... 16 2 8 3 2 4 2 2 2 1  W(2) 0 2 1  W‫א‬‫א‬‫א‬‫א‬  W(11001)‫א‬‫א‬  24 23 22 21 20 1 1 0 0 1 = (1 × 24) + (1 × 23) + (0 × 22) + (0 × 21) + (1 × 20) = 16 + 8 + 0 + 0 + 1 = (25)10 ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬(2)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K(11001)2‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ (Binary Digit)‫א‬(Bit)‫א‬‫ א‬W(Bit)‫א‬‫א‬■  ‫א‬E‫א‬F‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬   ‫א‬(4-bits)(1001)2‫א‬،‫א‬‫א‬  K‫א‬(7-bits)(1101101)2 -٤-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬ W(Number of Binary Combinations)‫א‬‫א‬■  K(bits)‫א‬‫א‬‫א‬‫א‬ N = 2n  W‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬= N W  (bits)‫א‬= n  W‫א‬‫א‬(2)‫א‬‫א‬ N = 22 = 4 N = 23 = 8 4 N = 2 = 16  W‫א‬‫א‬(3)‫א‬‫א‬  W‫א‬‫א‬(4)‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬W(Bit)‫א‬‫א‬■ ‫א‬(1)(1)20‫א‬‫א‬‫א‬‫א‬ 22‫א‬(2)21‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬(4)  ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬(LSB)‫א‬‫א‬(Least Significant Bit)   K(MSB)‫א‬‫א‬ (Most Significant Bit) ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬(Bit)‫א‬‫א‬WEByte) ‫א‬ ■  (0)‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬EF‫א‬‫א‬(1)‫א‬‫א‬  ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  ‫א‬  K -٥-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  (Byte)‫א‬ ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K 1 byte = 8 bits Decimal-to-Binary Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ (2)‫א‬‫א‬‫א‬‫א‬(Sum of Weights Method) ‫א‬‫א‬‫א‬ (Repeated Division–by–2 Method)  K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٤J ١ ‫א‬،214‫א‬،‫א‬(14)10‫א‬‫א‬   .(0)‫א‬2‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬،(MSB)‫א‬‫א‬‫א‬‫א‬(LSB)  W ‫ א‬ 14 ÷ 2 = 7 7 ÷2=3 3 ÷2=1 1 ÷2=0  0 1 1 1        1 1 1 0 (MSB) (LSB)  W (14)10 = (1110)2   K‫א‬(25)10‫א‬‫א‬WE١J ١F  W‫א‬ -٦-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬ 25 ÷ 2 = 12 12 ÷ 2 = 6 6 ÷2=3 3 ÷2=1 1 ÷2=0 1 0 0 1 1 (LSB) (MSB)  W‫א‬ (14)10 = (1110)2  K‫א‬(87)10‫א‬‫א‬WE٢J ١F   W‫א‬ ‫א‬ 87 ÷ 2 = 43 43 ÷ 2 = 21 21 ÷ 2 = 10 10 ÷ 2 = 5 5 ÷2=2 2 ÷2=1 1 ÷2=0 1 1 1 0 1 0 1 (LSB) (MSB)  W‫א‬ (87)10 = (1010111)2  ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٤J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ (Decimal Fractions)‫א‬‫א‬‫א‬K(2)‫א‬‫א‬  K(2)‫א‬‫א‬ 0.3125‫א‬‫א‬‫א‬‫א‬(0.3125)‫א‬‫א‬  ‫א‬‫א‬‫א‬(2)‫א‬‫א‬‫א‬،(2) (Carried Digits)‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬(0)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K(LSB)‫א‬‫א‬‫א‬(MSB)‫א‬‫א‬‫א‬K‫א‬  W  -٧-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬ 0.3125 × 2 = 0.625 0 0.625 × 2 = 1.25 1 0.25 × 2 = 0.5 0 0.5  × 2 = 1.00 1 (LSB) 1 0 1 0 (MSB) ‫א‬   ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬   KEF  K‫א‬(39.25)10‫א‬‫א‬WE٣J ١F  W(2)‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬   ‫א‬ 39 ÷ 2 = 19 19 ÷ 2 = 9 9 ÷2=4 4 ÷2=2 2 ÷2=1 1 ÷2=0  1 1 1 0 0 1 (LSB) (MSB)  W‫א‬     W(2)‫א‬‫א‬‫א‬‫א‬ (39)10 = (100111) 0.25 × 2 = 0.5 0.5 × 2 = 1.00   ‫א‬ 0 1  W (0.25)10 = (0.01)2  W‫א‬‫א‬‫א‬ -٨-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  (39.25)10 = (100111.01)2  Binary-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١ (2)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬K‫א‬16, 8, 4, 2, 1‫א‬‫א‬‫א‬‫א‬   (1)‫א‬‫א‬(Bit)‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬  K‫א‬1101001‫א‬‫א‬WE٤J ١F  ‫א‬‫א‬‫א‬‫א‬(1)W‫א‬ 26 25 24 23 22 21 20 : ‫א‬ 1 1 0 1 0  W 0 1 : ‫א‬‫א‬ = 1 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20 = 64 + 32 + 8 + 1 = (105)10 (Bits ) ‫ﺧﺎﻧ ﺎت‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ (Binary Point)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Decimal Point)‫א‬‫א‬ ……24 23 22 21 20 • 2-1 2-2 2-3 2-4…….  W  ‫א‬‫א‬   K‫א‬(0.1011)2‫א‬‫א‬‫א‬WE٥J ١F  • 2-1 0• 1 2-2 0 2-3 1  W‫א‬ 2-4 1 ∴(0.1011)2 = 1 × 2-1 + 1 × 2-3 + 1 × 2-4 = 0.5 + 0.125 + 0.0625 = (0.6875)10 -٩-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Binary Arithmetic ‫א‬‫א‬‫א‬‫א‬٦J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬  Binary Addition ‫א‬‫א‬١J ٦J ١ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ 0 0 1 1 + + + + 0 1 0 1 = = = = 0 1 1 0 carry E‫א‬F 1 ⇒ = 10  W(Binary Digits) ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬(1)‫א‬‫א‬،(2)1 + 1 = 10  W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  K011, 110‫א‬‫א‬WE٦J ١F   W‫א‬‫א‬‫א‬‫א‬W‫א‬ 1 6 +3 EF 9 4 +3 EF 7 + 1 1 1 0 0  1 1 0 0 1 1  K011, 100‫א‬‫א‬‫א‬WE٧J ١F  1 0 1 0 1 1 0 1 1 W‫א‬  Binary Subtraction ‫א‬‫א‬٢J ٦J ١  W‫א‬‫א‬  K‫א‬‫א‬‫א‬J ١ K‫א‬‫א‬J ٢ -١٠-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬K‫א‬‫א‬،‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬  0–0=0 1–0=1 1–1=0 0–1=1  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (1) ‫א‬ (1)‫א‬  W‫א‬‫א‬‫א‬  K‫א‬‫א‬ • W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K(0)‫א‬(1)(1)(0)(0) K(1)‫א‬(1)(0) ‫א‬F‫א‬‫א‬(0)(1)‫א‬(0)(1) K(0)(1)(1)E K‫א‬‫א‬‫א‬‫א‬‫א‬  K(011)‫א‬‫א‬(101)‫א‬‫א‬‫א‬WE٨J ١F  (0)‫א‬(1)‫א‬ ‫א‬‫א‬(1)‫א‬ (1)(10)‫א‬ 0 1  –0 0 (1)‫א‬  1 0       1 ‫א‬ 1 1 1 0 ‫א‬    W‫א‬       ‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١ One's and Two's Complements of Binary Numbers ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬(1)(0)(0)(1)‫א‬‫א‬  W‫א‬ -١١-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0  ‫א‬‫א‬ ‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬    ‫א‬ (1)‫א‬K‫א‬‫א‬W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬ 1 +‫א‬‫א‬Z‫א‬‫א‬ K10110011‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬(1)‫א‬‫א‬‫א‬ 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 + 1 0 1 0 0 1 1 1 0  ‫א‬‫א‬  ‫א‬‫א‬   ‫א‬‫א‬  (1)   ‫א‬‫א‬(LSB)‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ‫א‬‫א‬(0) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬  ،E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    W‫א‬‫א‬(10101101)2‫א‬‫א‬ ‫א‬‫א‬ 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1  ‫א‬‫א‬  ‫א‬‫א‬     Representation of Signed Numbers‫א‬‫א‬‫א‬‫א‬٨J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (1)،‫א‬(0)‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  -١٢-

‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬ (Sign Bit)‫א‬‫א‬‫א‬‫א‬  .(Magnitude) ‫א‬‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   .(2's Complement)‫א‬‫א‬ (1's Complement) ‫א‬‫א‬(Sign-Magnitude)  (Sign-Magnitude System) ‫א‬‫א‬١J ٨J ١ ‫א‬‫א‬‫א‬(Bit)‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (+23)‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ 0 0 0 1 0 1 1 1 ‫א‬ (Sign Bit)    ‫א‬‫א‬     (Magnitude Bits)  W ‫)32-( ﻓﺈﻧﻨﺎ‬‫א‬‫א‬     1 0 0 1 0 0 1 1 1  K‫א‬(–23) ، (+23)‫א‬‫א‬‫א‬  (1's Complement System) ‫א‬‫א‬٢J ٨J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

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