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NUMBERS DESCRIBE THE SYSTEM APPLYING BASIC DIGITAL ENGINEERING By Sri Wahyuni, S.Pd

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Teknologi dan Rekayasa DIRECTION Participant be able to: 1.Understanding the decimal number system 2.Understanding the binary number system 3.Understanding the number system octal 4.Understanding the hexadecimal number system 5.The number of conversion 6.The number of arithmetic operations 7.The code number used in a series of digital

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DECIMAL NUMBERS Number-based system 10 Numbers / digits used: 0,1,2,3,4,5,6,7,8,9 Value position: 10 3,10 2,10 1,10 0,10 -1,... Example: ( 1991) 10 = (1x 10 3 ) +(9x10 2 )+(9x10 1 )+(1x10 0 ) = 1x1000+9x100+9x10+1 = = 1991 Teknologi dan Rekayasa

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BINARY NUMBERS Number-based system 2 Numbers / digits used: 0 dan 1 Value position: ….2 5,2 4,2 3,2 2,2 1,2 0 … Example: (1001) 2 = = 1x2 3 +0x2 2 +0X2 1 +1x2 0 = = 9 Teknologi dan Rekayasa

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OCTAL NUMBERS Number-based system 8 Numbers / digits used: 0,1,2,3,4,5,6,7 Value position:.., 8 4, 8 3, 8 2, 8 1, 8 0, … Example: (27) 8 = 2x81+7x (23) 10 Teknologi dan Rekayasa

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HEXADECIMAL NUMBERS Number-based system 16 Numbers / digits used: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F A=10,B=11,C=12,D=13,E=14,F=15 Value position:..,16 3,16 2,16 1,16 0,16 -1,... Example: (11) 16 = 1x x16 0 = 16+1 = (17) 10 Teknologi dan Rekayasa

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CONVERSION NUMBERS 1.Decimal to binary conversion: a.(1001) 2=…………10 =1x2 3 +0x2 2 +0X2 1 +1x2 0 = =9 10 (Decimal) b.( 11011) 2 =………… 10 = = = (Decimal) Teknologi dan Rekayasa

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2.Binary to decimal conversion: 21/2 = 10 remain 1 10/2 = 5 remain 0 5/2 = 2 remain 1 2/2 = 1 remain 0 So: (21) 10 = (10101) 2 Teknologi dan Rekayasa

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3.Octal to decimal conversion : (27) 8 be converted to Decimal (27) 8 = 2 x x 8 0 = 2 x x 1 = = (23) 10 Teknologi dan Rekayasa

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4.Decimal to Octal conversion: (23) 10 be converted to Octal 23/8 = 2 remain 7 So : (23) 10 = (27) 8 Teknologi dan Rekayasa

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5.Conversion binary to octal To change the octal to binary, binary to be 3- bits. Example: ( ) 2 = = So : (101110) 2 = (136) 8 Teknologi dan Rekayasa

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6.Hexadecimal to Decimal Conversion (11) 16 be converted to Decimal (11)16 = 1 X X 16 0 = = (17) 10 Teknologi dan Rekayasa

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7.Hexadecimal to binary conversion To change to binary Hexadecimal, grouped into 4 bits starting from the LSB. Example: ( ) 2 = A D So: ( ) 2 = (1AD) 16 Teknologi dan Rekayasa

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8.Hexadecimal to binary conversion To change to binary Hexadecimal one by one in the hexadecimal number converted to 4-bit binary. Example: (13) 16 = So: (13) 16 = (10011) 2 Teknologi dan Rekayasa

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OPERATION WITH NUMBERS BINARY ARITHMETIC 1.Answer Numbers binary Terms: 0+0=0, remain 0 0+1=1, remain 0 1+0=1, remain 0 1+1=0, remain 1 Example: Teknologi dan Rekayasa

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2.The reduction in binary – be complement Teknologi dan Rekayasa

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3.The binary multiplication The binary multiplication is done with the Answer and a shift in the position of each step. Example: X 110 a.First Value: Teknologi dan Rekayasa

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b.Numbers Multiplier = 1, shift c.Numbers = 1 second, which multiplied in number and move the note Teknologi dan Rekayasa

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d.The to-3 = 1, and the number of sliding So, amount is: Teknologi dan Rekayasa

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4.The distribution of binary The division of the binary number with the same number of decimal. Teknologi dan Rekayasa

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Example: 111/ / So the result is: 1.11 Teknologi dan Rekayasa

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NUMBER CODES TO DIGITAL CIRCUIT 1.CODE BCD (BINARY CODE TO DECIMAL) Change the decimal to BCD Numbers Example: (678) 10 = So: (678) 10 = BCD Teknologi dan Rekayasa

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2.Change the BCD to Decimal Code. Example: BCD So: BCD = (5829) 10 Teknologi dan Rekayasa

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3.CODE Excess-3 This code is usually used to replace the BCD code. Example: (64) 10 Step 1: Add 3 to every Decimal digits Teknologi dan Rekayasa

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Step 2: The numbers of Answer amended to binary So: (64) 10 = Teknologi dan Rekayasa

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5.GRAY CODE Change Binary to GRAY. Example: (10110) Binary GRAY. Teknologi dan Rekayasa

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6.Change GRAY to Binary. Example: (101) GRAY Binary Teknologi dan Rekayasa

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The End Teknologi dan Rekayasa

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