3. Digital System: The physical quantities (signal) can assume
only discrete value.
Analog System: The physical quantities (signal) may vary
continuously over a special range.
Ex: o/p of digital system (0 or 5) voltage
Ex: o/p of analog system (-10,-9,..,0,9,10) voltage
4. Digital data
CD drive
10110011101
Analog
reproduction
of music audio
signal
Speaker
Sound
waves
Digital-to-analog
converter
Linear amplifier
Analog and Digital Systems
Many systems use a mix of analog and digital electronics to take
advantage of each technology. A typical CD player accepts digital
data from the CD drive and converts it to an analog signal for
amplification.
5. Signal
An information variable represented by physical
quantity (e.g., voltages and currents).
For digital systems, the variable takes on discrete
values.
Binary values are represented abstractly by:
1. digits 0 and 1
2. words (symbols) False (F) and True (T)
3. words (symbols) Low (L) and High (H)
4. and words On and Off.
6. Selected Key Terms
Analog
Digital
Binary
Bit
Being continuous or having continuous values.
Related to digits or discrete quantities; having a set
of discrete values.
Having two values or states; describes a number
system that has a base of two and utilizes 1 and 0
as its digits.
A binary digit, which can be a 1 or a 0.
7. bit , byte , word
bit (binary digit): the basic unit of memory
byte: 8 bits (e.g. 1010 1010 or 1000 0001)
word: 1, 2, 4 or 8 bytes (usually 4 or 8)
data and machine instructions are stored and accessed in
words (in memory)
1 Kilobyte (KB) = 1024 bytes = 210
bytes 103
bytes
1 Megabyte (MB) = 1024 KB = 220
bytes 106
bytes
1 Gigabyte (GB) = 1024 MB = 230
bytes 109
bytes
Examples:
CD-ROMs store around 650 Megabytes (MB)
DVDs store around 4.7 Gigabytes (GB), up to 17 GB
7
9. Number Systems
1- Decimal Numbers.
2- Binary Numbers.
3- Octal Numbers.
4- Hexadecimal Numbers.
1- Decimal Numbers: In the decimal number system
each of the ten digits (10digits), 0 through 9 (0, 1, 2, 3, 4,
5, 6, 7, 8, and 9).
Decimal weight … …104 103 102 101 100. 10-1 10-2 10-3 .
10. Example: Express the decimal number as a sum of the
values of each digits:
(47)10=(4*101) + (7*100)
(4*10) + (7*1) =47
(92.53)10 =
(9 x 101) + (2 x 100) + (5 x 10-1 ) + (3 x 10-2 ) =
(9 x 10) + (2 x 1) + (5 x 0.1 ) + (3 x 0.01 ) =
90 + 2 + 0.5 + 0.03 = 92.53
……102 101 100 • 10-1 10-2 10-3 ........
(Decimal Point)
11. 0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
10 1 0 1 0
11 1 0 1 1
12 1 1 0 0
13 1 1 0 1
14 1 1 1 0
15 1 1 1 1
Decimal
Number
Binary
Number
2-Binary Numbers: the binary number
system its two digits a base two system.
The two binary digits (bits) are 1 or 0
…22 21 20. 2-1 2-2 2-3 2-4 …
Binary point
A- Binary - to - Decimal conversion
25 24 23 22 21 20. 2-1 2-2
32 16 8 4 2 1 . ½ ¼
1 0 0 1 0 1 . 0 1
32 +4 +1 +¼ = 37¼
Convert the binary number 100101.01 to decimal.
12. (101.011)2 =
(1 x 22) +(0 x 21) + (1 x 20) + (0 x 2-1 ) + (1 x 2-2 ) + (1 x 2-3) =
(1 x 4) + (0 x 2) + (1 x 1) + (0 x 0.5 ) + (1 x 0.25 ) + (1 x 0.125) =
4 + 0 + 1 + 0 + 0.25 + 0.125 = 5.375
Convert from (205.188)10 to Binary Number Base Remainder
205 2 1
102 2 0
51 2 1
25 2 1
12 2 0
6 2 0
3 2 1
1 2 1
0(205.188)10=(11001101.00110 )2
0.188 x 2 = 0.376 carry = 0
0.376 x 2 = 0.752 carry = 0
0.752 x 2 = 1.504 carry = 1
0.504 x 2 = 1.008 carry = 1
0.008 x 2 = 0.016 carry = 0
Answer = .00110 (for five significant digits)
B- Decimal - to - Binary conversion
13. 3- Octal Numbers: The octal number system is composed of eight
digits, which are 0, 1, 2, 3, 4, 5, 6, and 7.
To count above 7, begin another column and start over:
10, 11, 12, 13, 14, 15, 16, and 17.
20, 21, 22, 23, 24, 25, 26, and 27…
Ex: (607.17)8
A- Octal – to – Decimal conversion:
Weight … … 83 82 81 80.8-1 8-2 8-3….
Example: Convert Octal number (2374)8 to decimal number
(2374)8 = 2*83 + 3*82 + 7*81 + 4*80
= 2*512 + 3*64 + 7*8 + 4*1
= 1024+192+56+4
= (1276)10
