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Digital

1. Digital Circuits
REZAN AHMAD
26 February 2023 1
Erbil Polytechnic University
Erbil Technology Institute
AIT department

2. Introduction of Digital Systems
Digitalsystemsusedigitalcircuitsthatprocessdigitalsignalswhich
cantakeononeoftwovalues,wecall:
0and1(digitsofthebinarynumbersystem)
or LOWandHIGH
or FALSEandTRUE
Digital Logic circuits handle data encoded in binary form, i.e. signals
that have only two values, 0 and 1.
2

3. • Analog information is made up of a continuum of values within a
given range
• At its most basic, digital information can assume only one of two
possible values: one/zero, on/off, high/low, true/false, etc.
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4. 4
Digital vs. Analog Waveforms
Analog systemshave inputs and
outputs that take on a continuous
range of values
Digital systemshave inputs and outputs
that are represented by discrete values
Binary digital systemshave exactly two
possible inputs /
output values, i.e., 0 or +5 V.+5
V
–5
T ime

5. 5

6. 1.Accuracy of results
2.More reliable than analog systems due to better immunity to
noise.
3.Ease of design
4.Digital signals use less power
5.Programmability.
6.Speed: A digital logic element can produce an output in
less than 10 nanoseconds (10
-8
seconds).
7.Economy: Due to the integration of millions of digital logic
elements on a single miniature chip forming low cost
integrated circuit (ICs).
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7. 7

8. 8
Allnumbersystemshaveabaseorradix,whichspecifieshow
manydigitscanbeusedineachplacecount.
Inthedecimalsystemthebaseis10,sotherearetendigitsthat
canbeusedforeachplacecount.Thedigitsare
0,1,2,3,4,5,6,7,8,9.
Forbinarynumbers,thebaseis2,with0and1astheonlytwo
digits.
Octalnumbersystem,thebaseis8,thismeansthatthedigits
usedisfrom0,1,2,3,4,5,6,7.
Hexadecimalnumbers,withabaseof16,thefirsttendigitsare
representedbythenumbers0,1,2,3,4,5,6,7,8,9,andtheletters
A,B,C,D,E,Fareusedtorepresentthenumbers10,11,12,13,
14and15respectively.

9. 9
The Decimal number system is a weighted number system.
For Integer decimal numbers, the weight of the rightmost digit (at position 0 )
is 1, the weight of position 1 digit is 10, that of position 2 digit is 100,
position 3 is 1000, etc.

10. Radix (base) = 10
MSD= Most Significant decimal
LSD= Least Significant decimal
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11. ⚫Base=2
⚫Two allowed digits {0,1}
⚫A Binary Digitis referred to as bit
⚫Examples: 1100011, 01, 0001, 11100
⚫The leftmost bit is called the Most Significant Bit (MSB)
⚫The rightmost bit is called the Least Significant Bit (LSB)
11010
Most Significant Bit
Least Significant Bit
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12. Converting fromDecimalto Binary
EX: Convert (80)10to Binary ?
2(80
2(400 LSB
2(200
2(100
2(50
2(21
2(10
(01 MSB
(80)10=(1010000)2
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13. 13

14. Converting from Binaryto Decimal:
EX: Convert (10010)
2to decimal ?
1 0 0 1 0
2
4
2
3
2
2
2
1
2
0
= 1x2
4
+0 x 2
3
+ 0x2
2
+ 1x2
1
+ 0x2
0
= (18)
10
14

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16. 16

17. 17

18. Base-16
Hexadecimal numbers are made of 16symbols:
(0,1,2,3,4,5,6,7,8,9,A, B, C, D, E, F)
Convert a hexadecimal number to decimal
(9AF)
16= 9x16
2 +
10x16
1 +
15x16
0
= (2479)
10
Note that each hexadecimal digit can be represented
with four bits.
(1011)
2 = (B)
16
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19. Converting from DecimaltoHexadecimal
EX: Convert (45)10to hexadecimal
16(45
16(213=D
(0 2
(45)10 =(2D)16
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21. 21
Converting from Hexadecimal toDecimal
EX: Convert (2A5)
16to decimal ?

22. 22

23. 23
EX: Convert (2A5)16 to decimal

24. 24
EX: Convert (2A5)16 to decimal