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

2. DIRECTION Participant be able to:
Understanding the decimal number system
Understanding the binary number system
Understanding the number system octal
Understanding the hexadecimal number system
The number of conversion
The number of arithmetic operations
The code number used in a series of digital
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3. DECIMAL NUMBERS Example: Number-based system 10
Numbers / digits used: 0,1,2,3,4,5,6,7,8,9
Value position: 103,102,101,100,10-1,...
Example:
(1991)10 = (1x 103) +(9x10 2)+(9x10 1)+(1x10 0)
= 1x1000+9x100+9x10+1 =
= 1991
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4. BINARY NUMBERS (1001)2= = 1x23+0x22+0X21+1x20 = 9 Example:
Number-based system 2
Numbers / digits used: 0 dan 1
Value position: ….25,24,23,22,21,20…
Example:
(1001)2=
= 1x23+0x22+0X21+1x20 =
= 9
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5. OCTAL NUMBERS (27)8 = 2x81+7x80 2+8+7+1 16+7 (23)10 Example:
Number-based system 8
Numbers / digits used: 0,1,2,3,4,5,6,7
Value position:.., 84, 83, 82, 81, 80, …
Example:
(27)8 =
2x81+7x80
16+7
(23)10
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6. HEXADECIMAL NUMBERS Example: (11)16 = 1x161 + 1x160 = 16+1 = (17)10
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:..,163,162,161,160,16-1,...
Example:
(11)16 = 1x x160
= 16+1
= (17)10
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7. CONVERSION NUMBERS Decimal to binary conversion: (1001)2=…………10
=1x23+0x22+0X21+1x20 =
=910 (Decimal)
( 11011)2=…………10 = =
= 2710 (Decimal)
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8. Binary to decimal conversion: 21/2 = 10 remain 1
So:
(21)10 = (10101)2
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9. Octal to decimal conversion : (27)8 be converted to Decimal
(27)8 = 2 x x 80
= 2 x x 1 =
= (23)10
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10. Decimal to Octal conversion: (23)10 be converted to Octal
23/8 = 2 remain 7
So :
(23)10 = (27)8
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11. Conversion binary to octal
Conversion binary to octal To change the octal to binary, binary to be 3-bits.
Example:
( )2 = =
So :
(101110)2 = (136)8
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12. Hexadecimal to Decimal Conversion (11)16 be converted to Decimal
(11)16 = 1 X X 160 =
= (17)10
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13. 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
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14. 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
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15. OPERATION WITH NUMBERS BINARY ARITHMETIC
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:
1110
0101 +
10011
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16. The reduction in binary 1001 1001 0111 – be complement 1000 +
0111 – be complement
10001
1 +
0010
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17. The binary multiplication The binary multiplication is done with the Answer and a shift in the position of each step.
Example:
10101 X 110
First Value:
00000
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18. 00000 Numbers Multiplier = 1, shift
Numbers = 1 second, which multiplied in number and move the note.
10101
101010
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19. The to-3 = 1, and the number of sliding 101010 10101 1111110
So, amount is:
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20. The distribution of binary The division of the binary number with the same number of decimal.
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21. So the result is: Example: 1.11 111/100 100/ 1.11 111 -100 110 100 000
100/ 1.11
111
-100
110
100
000
So the result is:
1.11
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22. NUMBER CODES TO DIGITAL CIRCUIT
CODE BCD (BINARY CODE TO DECIMAL) Change the decimal to BCD Numbers
Example:
(678)10 =
So:
(678)10 = BCD
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23. Change the BCD to Decimal Code. Example: BCD 0101100000101001
So:
BCD = (5829)10
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24. CODE Excess-3
This code is usually used to replace the BCD code.
Example:
(64)10
Step 1:
Add 3 to every Decimal digits
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25. The numbers of Answer amended to binary 9 7 1001 0111 So:
Step 2:
The numbers of Answer amended to binary
So:
(64)10 =
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26. GRAY CODE Change Binary to GRAY. Example: (10110)2 1 0 1 1 0 Binary
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27. Change GRAY to Binary. Example: (101) 1 1 0 1 GRAY 1 0 0 1 Binary
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28. The End
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