# NUMBERS DESCRIBE THE SYSTEM

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

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 Teknologi dan Rekayasa

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 Teknologi dan Rekayasa

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 Teknologi dan Rekayasa

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 Teknologi dan Rekayasa

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 Teknologi dan Rekayasa

CONVERSION NUMBERS Decimal to binary conversion: (1001)2=…………10
=1x23+0x22+0X21+1x20 = =910 (Decimal) ( 11011)2=…………10 = = = 2710 (Decimal) Teknologi dan Rekayasa

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

Octal to decimal conversion : (27)8 be converted to Decimal
(27)8 = 2 x x 80 = 2 x x 1 = = (23)10 Teknologi dan Rekayasa

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

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 Teknologi dan Rekayasa

Hexadecimal to Decimal Conversion (11)16 be converted to Decimal
(11)16 = 1 X X 160 = = (17)10 Teknologi dan Rekayasa

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

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

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 Teknologi dan Rekayasa

The reduction in binary 1001 1001 0111 – be complement 1000 +
0111 – be complement 10001 1 + 0010 Teknologi dan Rekayasa

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 Teknologi dan Rekayasa

00000 Numbers Multiplier = 1, shift
Numbers = 1 second, which multiplied in number and move the note. 10101 101010 Teknologi dan Rekayasa

The to-3 = 1, and the number of sliding 101010 10101 1111110
So, amount is: Teknologi dan Rekayasa

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

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

Change the BCD to Decimal Code. Example: BCD 0101100000101001
So: BCD = (5829)10 Teknologi dan Rekayasa

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

The numbers of Answer amended to binary 9 7 1001 0111 So:
Step 2: The numbers of Answer amended to binary So: (64)10 = Teknologi dan Rekayasa

GRAY CODE Change Binary to GRAY. Example: (10110)2 1 0 1 1 0 Binary
Teknologi dan Rekayasa

Change GRAY to Binary. Example: (101) 1 1 0 1 GRAY 1 0 0 1 Binary
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The End Teknologi dan Rekayasa

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