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

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Presentation on theme: "NUMBERS DESCRIBE THE SYSTEM APPLYING BASIC DIGITAL ENGINEERING By Sri Wahyuni, S.Pd."— Presentation transcript:

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

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

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

11 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

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

13 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

14 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

15 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

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

17 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

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

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

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

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

22 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

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

24 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

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

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

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

28 The End Teknologi dan Rekayasa


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