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Digital system design
Digital Systems
Digital vs. Analog Waveforms
+5
+5
1
0
1
V
V
Time
–5
Digital:
only assumes discrete values
Time
–5
Analog:
values vary over a broad range
continuously
Digital signal status
Wave form
Decimal base 10
Binary base 2
Hexadecimal base 16
From decimal to binary
Surplus
Surplus
Surplus
Surplus
Decimal to hexadecimal
Surplus
Surplus
Surplus
Binary to Hexadecimal
Hexadecimal to Binary
Binary characteristics
Transform
2. Mathemmatic of binary:
a. Add :
0
0
1
1
+
+
+
+
0
1
0
1
=
=
=
=
1
0
1
1
0 nhớ 1
1
1
1 0 1 1 1
1 0 1
1 1 1 0 0
b. Subtract:
0
0
1
1
-
0
1
0
1
=
=
=
=
-1 -1 -1
0
1 mượn 1
1
0
1 1 0 1 0
1 1 1
1 0 0 1 1
13
1 0 1 1
1 0 0 1
c. Multiply:
1 0 1 1
0 0 0 0
0 0 0 0
1 0 1 1
1 1 0 0 0 1 1
d. Divide:
1 0 0 1
1 0 1
1 1
1 0
0 0 0 1
1
1 0
1 1
1 1 0 1
1 0 1 1
1 0
14
1 0 1 1
1 1 0 1
2. Signed Binary Arithmetic:
- Like signed decimal Arithmetic .
- The calculation and result must have similar number of
bits
- If result are not in the bit range, should increase the
number of bits of the calculation)
-6
+
+3
-3
+4 :
+
+5 :
-7 :
: 1010
: 0011
: 1101
0100
0101
1 0 0 1 (Wrong)
-2 : 1110
+
-5 : 1011
-7 : 1001
00100
00101
0 1 0 0 1 : + 9 (Correct)
-6
-2
-4
:
:
:
+2
:
-5 :
+7 :
1010
1110
1100
-7 : 1001
+5 : 0101
+ 4 : 0 1 0 0 (Kq sai)
0010
1011
0111
11001
00101
1 0 1 0 0 : - 12 (Kq đúng)
16
d. Mã ký tự ASCII:
20
Seven Segment Displays
This presentation will demonstrate how
A seven-segment display can be used to display the decimal
numbers 0-9 and some alpha characters.
A common anode seven-segment display works.
A common cathode seven-segment display works.
To select the resistor value for a seven-segment display.
Retro
LED Watch
(Circa 1970s)
21
a
g
f
b
c
e
d
a
g
f
b
c
e
d
Truth Tables for logic operators
Truth table: tabular form that uniguely represents the relationship
between the input variables of a function and its output
2-Input AND
A
0
0
1
1
B F=A•B
0 0
1
0
0 0
1
1
2-Input OR
A
0
0
1
1
B F=A+B
0 0
1
1
0 1
1
1
NOT
A F=A’
0
1
1
0
Truth Tables (cont.)
Q: Let a function F() depend on n variables.
How many rows are there in the truth table of
F() ?
n
n
A: 2 rows, since there are 2 possible binary
patterns/combinations for the n variables
