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C arch presentation1
1.
2.
2.1.NUMBER SYSTEM 2.1.1.Binary System Binary
α α α α α α α α α α α αα α α2 α αα α α0 α α α α α α α α α α α α α α α α α α α α α α1 α οΆ α α α α αDecimal α α α α Binary Example : N = (85)10 α α α α α Binary α α α α 85 2 01 42 2 00 21 2 01 10 2 0 5 2 1 2 2 0 1 2 1 0 α α α α α α N = (85)10 =(1010101)2
3.
α α α
α α BINARY α α α α α DECIMAL Example : N =(1010101)2 Decimal N = 1 x 26 + 0 x 25 + 1 x 24 + 0 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 64 + 32 x 0 + 16 + 0 + 4 + 0 + 1 = 85 α α α N = (1010101)2 = (85)10 α α α A . α α α α α α α (addition)α αBinary α α α α α α α α - α α α α α α α α α Binary α α α αα α α α α α Decimal α α α α α α α α α α α α α α α α α α α α α α α α α α 0+0=0 0+1=1 1+0=1 1+1=0 α α α α α α α α α αCarry 1) = 10
4.
EXAMPLE : 10101
B + 10100 B 10101 + 10100 101001 B. α α α α α α α α α α α αSubtraction) α α α α Binary α α α αα α α α α α α α α α α α α α α αDecimal α α α α α α α α α α α α α α α 0β0=0 1β1=0 1β0=1 0 β 1 = 1 α α α α 1 (carry 1) α α α Example a : 1100110 b β 110110 b Solution : 1100110 β 110110 0110000
5.
C. α α
α α α α α MULTIPLICATION) α α α α α α α α α α Binary α α α αα α Decimal α α α α α α α α α α α α α α α α α α α α α 0x0=0 1x0=0 0x1=0 1x1=1 Example : A. 101011b x 1100b 101011 1100 101011 101011 1000000100
6.
D. α α
α α α α α(DIVISION) α α α α α α α α α α αBinary α α α α α α α α α α α Decimal α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α αBinary α α α α α α α α α α α 0/1 = 0 1/1 = 1 Example: A . 11011b/101b Solution 11011 101 101 101 0011 000 111 101 010
7.
2.1.2 . OCTAL
SYSTEM α α α α α α α α α α αα α α α 8 α α 0, 1 , 2β¦β¦.. 7 α α α α α α α α α α α α α α α α α α 8α α α α α α α α α α α α α α α α α α οΆ α α α α α α 8 α α α 10 (Decimal) α α α α α α α Decimal = On 8n +β¦β¦β¦β¦.+O2 81 + O1 80 α αOn α α α α α α α Octal α α α α α α α α α α α α α α α α α α α α α α α α α α α α α Example : α α α α Octal α α α α Decimal A .(765)8 Solution : A = (765)8 Decimal = 7 x 82 + 6 x 81 + 5 x 80 = 7 x 64 + 48 + 5=(501)10 A . α α α α α α α α Addition) α α α α α α α α Example: a (2456)8 + (1276)8 Solution 2456 + 1276 3754
8.
B . α
α α α α α SUBTRACTION) α α α α α α Example: a , (4567)8 β (1075)8 Solution 4567 - 1075 3472 C . α α α α α α αMultiplication) α α α α α α Example a, (1234)*(12) Solution: 1234 * 12 2470 1234 15030
9.
α α α
α α α αDIVISION α α α α α α α α α α α α α α α α α α α octalα α α α α α α α α α α α α α α α α α α α α α α α α decimal α α α Example: a , (502)8 / (27)8 Solution 502 27 27 16 212 212 000
10.
2.1.3. HEXADECIMAL SYSTEM
α α α α α α α α α Hexa α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α α16 α α α α0 ,1 ,2 ,3β¦β¦A ,B α α α α α α ,F=15) α α16 α α οΆ ,C α ,Eα α α B=11,α10 D=13 ,E=14 16 α,D α,F(A=10,α α C=12, α α α α α α α α Example: a , α α α5760)10 α α α α 16 α Solution 5760 16 48 360 16 096 32 22 16 96 40 6 1 16 0 32 0 8 a : (5760)10 = (1680)16
11.
οΆ α α
α α αHEXA α α α α DECIMAL Example: a =(1680)16 Decimal Solution Decimal : 160 x 0 + 161 x 8 + 162 x 6 + 163 x 1 = 0 +128 + 1536 + 4096 =(5760)10 A . α α α α α α α(Addition) α α α α α α Example: a, 76BC H + A76B H 76BC + A76B 11E27
12.
B. α α
α α α α α α α α α αSUBTRACTION) Example: a, 2B75 H β 10EF 2B75 - 10EF 1A86 C .α α α α α α α Multiplication) α α α α α α Example: 26AF H x 12 H Solution 26AF x 12 4C5E 26AF 2B84E
13.
D .α α
α α α α αDIVISION) α α α α α α Example : a, AB5 H/A1 Solution AB5 A1 A1 11 0A5 A1 04 α α α a= 11 α α α
14.
α α α
α α α α α α α α α α Decimal Hexa Binary 0 0 0000 1 1 0001 2 2 0010 3 3 0011 4 4 0100 5 5 0101 6 6 0110 7 7 0111 8 8 1000 9 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111
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