LOGIC1_r2 - Chapter 1 Introduction Microwave &...

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Chapter 1 Introduction
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(a)Decimal Number (Base 10 , i.e., 0,1,2,3,4,5,6,7,8,9) EX 10 2 10 1 10 0 10 -1 10 -2 ( 9 5 3 . 7 8 ) 10 =9*10 2 +5*10 1 +3*10 0 +7*10 -1 +8*10 -2 (b)Binary Number (Base 2 , i.e.,0,1) EX 2 3 2 2 2 1 2 0 2 -1 2 -2 ( 1 0 1 1 . 1 1 ) 2 =1*2 3 +0*2 2 +1*2 1 +1*2 0 +1*2 -1 +1*2 -2 =8+0+2+1+1/2+1/4=(11.75) 10 §Number Systems
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(c)Octal Number (Base 8 , i.e.,0,1,2,3,4,5,6,7) EX 8 2 8 1 8 0 8 -1 ( 1 4 7 . 3 ) 8 =1*8 2 +4*8 1 +7*8 0 +3*8 -1 =64+32+7+3/8=(103.375) 10 (d)Hexadecimal (Base 16 , i.e,0,1,2 9,A,B,C,D,E,F) EX 16 2 16 1 16 0 ( A 2 F ) 16 =10*16 2 +2*16 1 +15*16 0 =2560+32+15=(2607) 10
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Remark: Any positive integer R(R>1)can be chosen as the radix or base of a number system. If the base is R , then R digits (0,1,2,……R-1)are used. For a R based number N N=(a n a n-1 …… a 1 a 0 . b 1 b 2 b 3 …… b m ) R =a n R n +a n-1 R n-1 +…+a 1 R 1 +a 0 R 0 +b 1 R -1 +b 2 R -2 +… +b m R -m
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§ Conversions (a) Radix-R to decimal conversion Directly factoring the power expansion (a n a n-1 …a 1 a 0 .b 1 b 2 …b m ) R =a n R n +a n-1 R n-1 +…+a 1 R 1 +a 0 R 0 +b 1 R -1 +b 2 R -2 +…b m R -m =(c i c i-1 …c
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LOGIC1_r2 - Chapter 1 Introduction Microwave &...

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