DIGITAL SYSTEM

System analog / digital processing the signals vary with time
have the values ​​of continuous / discrete as shown in Figure 1.
Figure 1: The analog signal vs. discrete signals
Some of the advantages of digital systems compared to analog systems are:
- The ability to reproduce a better signal and accurate
- Have a better reliability (due to lower noise immunity
better)
- Easy in design, requiring no special mathematical skills to
visualize the properties of a simple digital circuit
- Flexibility and better functionality
- Programming skills easier
- Faster (complete debug complex digital ICs can produce a
output is less than 2 nano seconds)

- Economical if viewed in terms of the cost of the IC will be low due to
repetition and mass production of the integration of millions of digital logic elements
on a single miniature chip.
Digital systems using combinations of binary TRUE and FALSE
to resemble the way when solving a problem that is also called logikalogika
combinational. With a digital system can be used step-by-step thinking
logical or decisions of the past (memory) to solve the problem
so-called sequential logics (sequences).
Digital logic can be represented in several ways, namely:
- The truth table (truth table) provides a list of every combination
which may be of binary inputs on a digital circuit
and outputs are related.
- Boolean expressions to express the logic in a format
functional.
- Diagram logic gates (logic gate diagrams)
- Placement diagrams parts (parts placement diagrams)
- High level description language (HDL)

2. NUMBER SYSTEM AND CODING
2.1 Number Systems
Some number systems:
1. Decimal Numbers
Decimal number is a number that has a base 10
These numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 (r = 10)
2. Binary Numbers
Binary number is a number that has a base of 2
These numbers are 0 and 1 (r = 2)
3. Octal Numbers
Octal number is a number that has a base of 8
These numbers are 0, 1, 2, 3, 4, 5, 6, and 7 (r = 8)
4. Hexadecimal Numbers
Hexadecimal numbers are numbers that have a base 16
These numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F (r = 16)
2.2 Conversion of Numbers
1. Convert Decimal Numbers to Binary Numbers
Decimal value divided by 2, reading the final value of the division
and the order of the rest of the division is a binary form of the decimal value.
2. Converting Binary Numbers to Decimal Numbers
Each sequence of binary values ​​are summed, with the first value
The binary binary numbers are multiplied by the weight of each.
example:
Change the binary number into decimal number 1001
Answer:
(1x23) + (0x22) + (0x21) + (1x20) ≡
(1x8) + (0x4) + (0x2) + (1x1) ≡
8 + 0 + 0 + 1 = 9
So the result of the conversion of the binary number 1001 is 9 decimal.
3. Converting Octal Numbers to Decimal Numbers
Decimal value divided by 8, the reading of the final value of the division
and the order of the rest of the division is the octal form of a decimal value.
4. Converting Octal Numbers to Decimal Numbers
Each sequence of octal values ​​are summed, with the first value
The octal octal number is multiplied by the weighting of each.
example:
1021 Change octal numbers into decimal numbers
Answer:
(1x83) + (0x82) + (2x81) + (1x80)
(1x512) + (0x64) + (2x8) + (1x1)
512 + 0 + 16 + 1 = 529
4
So the conversion of octal number 1021 is 529 decimal.
5. Convert Decimal Numbers to Hexadecimal Numbers
Divided by the value of the decimal number 16, the reading of the final value of the division
and the order of the rest of the division is a form of Hexadecimal number of values
decimal.
6. Convert Decimal Numbers to Hexadecimal Numbers
Each sequence of hex numbers summed value, the first value
multiplied by the weight of the hex hexadecimal numbers respectively.
example:
Change the hex numbers into decimal 9AF
Answer:
(9x162) + (Ax161) + (Fx160)
(9x162) + (10x161) + (15x160)
2304 + 160 + 15 = 2479
So the conversion of hex number is 2479 decimal 9AF
7. Converting Octal to Binary Numbers
Each octal digit numbers can be represented in a 3-digit number
binary. Each octal digit number be changed separately.
example:
Convert octal number 3527 into binary numbers
Answer:
3 5 2 7
011 101 010 111
5
So the conversion of octal number is 011 101 010 111 3527
8. Converting Binary to Octal number
Grouping each three-digit binary numbers ranging from LSB to MSB.
Each group will signify octal value of that number.
example:
Convert binary numbers into octal 11110011001
Answer:
011 110 011 001
3 6 3 1
So the result of the conversion of a binary number is 11110011001 3631
9. Converting Hexadecimal Numbers to Binary number
Each digit hex numbers can be represented in the 4-digit numbers
binary. Each digit hex numbers changed separately.
example:
Convert hex numbers into binary numbers 2ac
Answer:
2 A C
0010 1010 1100
So the conversion of hex numbers 2ac is 001 010 101 100
10. Converting Binary to Hexadecimal
Grouping each four-digit binary number ranging from LSB to MSB.
Each group will mark the hex value of the number.
example:
Change the binary number into hex numbers 10011110101
Answer:
4 F 5
0100 1111 0101
So the result of the conversion of a binary number is 10011110101 4F5
6
Binary Numbers 2.3 Fractions
1. Conversion of decimal numbers into binary fractions
Multiplying the fractional part of the decimal number by 2, section
rounded by multiplying the fractional nature of binary bits.
example:
Change the binary number into a binary number 0,625
Answer:
0,625 x 2 = 1.25 rounded part = 1 (MSB), residual = 0.25
0.25 x 2 = 0.5 rounded part = 0, the rest = 0.5
0.5 x 2 = 1.0 rounded part = 1 (LSB), the rest = 0
So 0.625 = 0.101
2. Convert binary numbers into decimal fractions
Multiplying each bit binary number after the decimal (fractional) with weights
of each bit of the number.
example:
Change the binary number into decimal number 0,101
Answer:
(1x2-1) + (0x2-2) + (1x2-3)
(1x0,5) + (0x0,25) + (1x0,125)
0.5 + 0 + 0.125 = 0.625
So 0.101 = 0.625
2.4. Numbers Binary Coded Decimal (BCD)
BCD revealed that each decimal digit as a
nibble. Nibble is a string of 4 bits.
Example 1:
Specify the number of decimal BCD 2954
Answer:
2 9 5 4
0010 1001 0101 0100
So, the decimal number is 0010 1001 2954 0101 0100 BCD
Example 2:
Determine the decimal number of BCD 101001110010111
Answer:
7
0101 0011 1001 0111
5 3 9 7
So, BCD 101001110010111 is 5397 decimal.
2.5. Binary arithmetic
1. Binary Addition
The basic rules of binary addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, store 1
example:
Add up the binary number 11001 to 11011
Answer:
11001
11011
110 100
So the sum is 11001 to 11011 110 100
2. Reduction of Binary
The basic rules of binary subtraction
0-0 = 0
1-0 = 1
1-1 = 0
0-1 = 1, borrow 1
Example: Subtract binary numbers 1111 to 0101
Answer:
1111
0101
1010
So the result is a reduction in 1111 to 0101 in 1010
2.6. Complement binary numbers 1 and 2 complement
Complement binary number 1 can be obtained by replacing all bits 0
to 1, and all bits 1 to 0.
Example: Determine the binary complement of the binary number 100101 1
+
8
Answer:
Binary number: 100101
Complement binary number 1: 011 010
Complement binary number 2 can be obtained by adding 1 to the number
complement binary 1.
Example: Define two binary complement of the binary number 100101
Answer:
Binary number: 100101
Complement binary number 1: 011 010
+ 1
Complement binary number 2: 011 011
Complement binary number 2 can be used for the reduction of binary numbers.
2.7. Gray code
Gray code is typically used in mechanical encoder. For example, the telegraph.
1. Convert binary to gray code
There are several steps to convert a binary number into Gray code:
a. Write down the binary number
b. MSB MSB binary number is the gray code
c. Sum (using modulo2) first bit binary number
the second bit, the result is the second bit gray code.
d. Repeat steps c to bits the next.
Example: Change the binary number 1001001 into the gray code
Answer:
Binary Gray Description
1001001
1001001 1 = MSB MSB Binary Gray
1001001 11 1 modulo2 0 = 1
Modulo2 1001001 110 0 0 = 0
1001001 1101 0 modulo2 1 = 1
1001001 11011 1 modulo2 0 = 1
Modulo2 1001001 110110 0 0 = 0
1001001 1101101 0 modulo2 1 = 1
So the gray code of the binary number 1001001 is 1101101
2. Converting gray code to binary numbers
There are several steps to convert gray code into binary numbers:
a. Write down the binary number
b. MSB MSB is a gray code binary number
c. Sum (using modulo2) first bit gray code by
second bit binary numbers, the result is the second bit binary number.
d. Repeat steps c to bits the next.
Example: Change the gray code into binary number 1101101
Answer:
Binary Gray Description
1101101
1101101 1 = MSB MSB Binary Gray
1101101 10 1 modulo2 1 = 0
Modulo2 1101101 100 0 0 = 0
1101101 1001 0 modulo2 1 = 1
1101101 10010 1 modulo2 1 = 0
Modulo2 1101101 100100 0 0 = 0
1101101 1001001 0 modulo2 1 = 1
So the binary number of the gray code 1101101 is 1001001
2.8. Excess-3 Code
Excess-3 code is obtained by summing the decimal values ​​by 3, then
converted into a binary number.
Decimal Binary Excess-3
0 0000 0011
1 0001 0100
2 0010 0101
3 0011 0110
4 0100 0111
5 0101 1000
6 0110 1001
7 0111 1010
8 1000 1011
9 1001 1100
10
3. BASIC DIGITAL
3.1. The gates of digital systems
The gates of a digital system or logic gates are devices that have
logic level state. Logic gates can represent the state of a number
binary.
There are two state of the logic gates, namely 0 and 1. The voltage
used in logic gate is HIGH (1) and LOW (0). Digital systems
The most complex as a large computer composed of basic logic gates such as AND,
OR, and NOT gates combination (derivative) is composed of the basic gates
such as NAND, NOR, EXOR, EXNOR.
Universal Gate is a gate that is coupled derivative
so as to produce the same output with the output of the base gates and
derivative gate. As it is a universal gate NAND and NOR.
AND gate is used to generate a logic 1 when all inputs
is logic 1. The OR gate is used to generate a logic 1 if either
the input logic 1. The gate is not a gate inverter (inverting). output
produced is the inverse of a given input. Derivative logic gates.
3.2 Integrated circuit
The integrated circuit is formed of a series of applications of various kinds
logic gates. The integrated circuit can be a combination of one type
logic gates or more. Simplification of integrated circuits can be used
boolean algebra theorem and or map karnough.