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Pertemuan 1 Teknik Digital 1

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- Digital Electronics
- Number Systems and Logic
- Electronic Gates
- Combinational Logic
- Sequential Circuits
- ADC – DAC circuits
- Memory and Microprocessors
- Hardware Description Languages

- Digital vs Analog data
- Binary inputs and outputs
- Binary, octal, decimal and hexadecimal number systems
- Other uses of binary coding.

- Analogue Systems
- V(t) can have any value between its minimum and maximum value

V(t)

- Digital Systems
- V(t) must take a value selected from a set of values called an alphabet
- Binary digital systems form the basis of almost all hardware systems currently

V(t)

1

0

1

0

1

For example, Binary Alphabet: 0, 1.

- Consider a child’s slide in a playground:

a set of discrete steps

continuous movement

levels

5 Volt

Input

Range

for 1

Output

Range

for 1

2.8

2.4

0.8

Input

Range

for 0

Output

Range

for 0

0.4

0 Volt

- Advantages of Digital Systems
- Analogue systems: slight error in input yields large error in output
- Digital systems more accurate and reliable
- Computers use digital circuits internally
- Interface circuits (for instance, sensors and actuators) are often analogue

- Coding:
- A single binary input can only have two values: True or False (Yes or No) (1 or 0)

- More bits = more combinations

0 0 0 1 1 0 1 1

- Each additional input doubles the number of combinations we can representi.e. with n inputs it is possible to represent 2n combinations

- Example 1:
- How many combinations are possible with 10 binary inputs?

- Example 2:
- What is the minimum number of bits needed to represent the digits ‘0’ to ‘9’ as a binary code?”

- Number Representation
- Difficult to represent Decimal numbers directly in a digital system
- Easier to convert them to binary
- There is a weighting system:

eg

403 = 4 x 100 + 0 x 10 + 3 x 1

or in, powers of 10:

40310= 4x102 + 0x101 + 3x100 = 400 + 0 + 3

- Both Decimal and Binary numbers use a positional weighting system, eg: 10102 = 1x23+0x22+1x21+0x20 = 1x8 + 0x4 + 1x2 + 0x1 = 1010

- Multiply each 1 bit by the appropriate power of 2 and add them together.

100000112 = ……………….10 ?

1010011002 = ……………………10 ?

- Number Representation - Binary to decimal
- A decimal number can be converted to binary by repeated division by 2

15510 = 100110112

An alternative way is to use the “placement” method

128 goes into 155 once leaving 27 to be placed

So 64 and 32 are too big (make them zero)

16 goes in once leaving 11

and so on…

- There are different ways of representing decimal numbers in a binary coding
- BCD or Binary Coded Decimal is one example.
- Each decimal digit is replaced by 4 binary digits

- 6 of the possible 16 values unused
- example 45310 = 0100 0101 0011BCD
- Note that BCD code is longer than a direct representation in natural binary code:
- 453 = 111000101

- Hexadecimal and Octal
- Writing binary numbers as strings of 1s and 0s can be very tedious
- Octal (base 8) and Hexadecimal (base 16) notations can be used to reduce a long string of binary digits.

Notice that hexadecimal requires 15 symbols (each number system needs 0 – base-1 symbols) and therefore A – F are used after 9.

- Each octal digit corresponds to 3 binary bits

To convert a binary string: 10011101010011

Split into groups of 3:

010 011 101 010 011

2 3 5 2 3

Thus 100111010100112 = 235238

- Each hex digit corresponds to 4 binary bits

To convert a binary string: 10011101010011

Split into groups of 4:

0010 0111 0101 0011

Thus 100111010100112 = ……………16 ?

- Colour codes
- You often see hex used in graphic design programs for the red, blue and green components of a colour:
- FF0000 represents red, for example.
- How many bits are used to represent each colour?
- How many different colours can be represented?

- Characters
- Three main coding schemes used: ASCII (widespread use), EBCDIC (not used often) and UNICODE (new)
- ASCII table (in hex) :

- Other codes exist for specific purposes
- Gray codes provide a sequence where only one bit changes for each increment
- Allows increments without ambiguity due to bits changing at different times.
- E.g. changing from 3 to 4, normal binary has all three bits changing 011 -> 100. Depending on the order in which the bits change any intermediate value may be created.

- Support website
- Analogue and Digital
- Binary Number Systems
- Coding schemes considered were:
- Natural Binary
- BCD
- Octal representation
- Hexadecimal representation
- ASCII

- You should practice conversions between binary, octal, decimal and hexadecimal.
- You should be able to code decimal to BCD (and BCD to decimal).
- You should be able to explain and give examples of digital and analogue data.