DIGITAL CIRCUIT DIGITAL CIRCUIT DESIGN DESIGN EEE122 A EEE122 A Ref. Morris MANO & Michael D. CILETTI Ref. Morris MANO & Michael D. CILETTI DIGITAL DESIGN 4 DIGITAL DESIGN 4 th th edition edition Fatih University- Faculty of Engineering- Electric and Electronic Dept.
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DIGITAL CIRCUIT DIGITAL CIRCUIT DESIGNDESIGN
EEE122 AEEE122 A
Ref. Morris MANO & Michael D. CILETTIRef. Morris MANO & Michael D. CILETTI
DIGITAL DESIGN 4DIGITAL DESIGN 4thth editionedition
Fatih University- Faculty of Engineering- Electric and Electronic Dept.
WHAT IS DIGITAL CIRCUITWHAT IS DIGITAL CIRCUIT
�� Engineers generally classify electronic Engineers generally classify electronic
circuits as being either analog or digital.circuits as being either analog or digital.
�� Analog circuit works with sinusoidal Analog circuit works with sinusoidal
signalssignals
�� Digital circuit works with discrete signalsDigital circuit works with discrete signals
�� Today Most electronic devices are Today Most electronic devices are
composed of digital circuitscomposed of digital circuits
Advantages of Digital over Analog CircuitAdvantages of Digital over Analog Circuit
�� Easier to design using integrated Easier to design using integrated
circuitcircuit
�� Have very effective information Have very effective information
storagestorage
�� Can be programmed to suite the Can be programmed to suite the
required situationrequired situation
�� More accurate and of less affected by More accurate and of less affected by
electromagnetic noiseselectromagnetic noises
APPLICATION OF DIGITAL CIRCUITAPPLICATION OF DIGITAL CIRCUIT
�� Digital CalculatorsDigital Calculators
�� Computer systemsComputer systems
�� Robot systemRobot system
�� Measurement devicesMeasurement devices
�� Telecommunication systemsTelecommunication systems
�� 1: Sum1: Sum--ofof--weights methodweights method•• To get the binary number for a given To get the binary number for a given decimal number, find the binary weights decimal number, find the binary weights that add up to the decimal number.that add up to the decimal number.
•• Repeated multiplication by 2Repeated multiplication by 2
�� Decimal fraction can be converted to binary Decimal fraction can be converted to binary
by by repeated multiplication by 2repeated multiplication by 2
Repeated Multiplication by 2 Repeated Multiplication by 2
�� ex: convert the decimal fraction 0.3125 to binaryex: convert the decimal fraction 0.3125 to binary
carrycarry
111.1. 0000==0.0. 5050 x 2x 2
000.0. 5050==0.0. 2525 x 2x 2
111.1. 2525==0.0. 625625 x 2x 2
000.0. 625625==0.3125 x 20.3125 x 2
Continue to the desired number of decimal places or stop when the fractional part is all zero
MSB
LSB
0.31250.3125 1010 = 0.0101= 0.0101 22
Hexadecimal and Octal Hexadecimal and Octal NumbersNumbers
HexadecimalHexadecimal (hex)(hex) NumbersNumbers
It composed of 16 characters. Digits It composed of 16 characters. Digits 00--99and letters and letters A, B, C, D, E, & FA, B, C, D, E, & F representing representing the numbers from 10 the numbers from 10 --toto-- 15.15.
�� It used as a compact method to express or It used as a compact method to express or display binary numbers.display binary numbers.
�� Hexadecimal is commonly used in Hexadecimal is commonly used in microprocessor impeded systems.microprocessor impeded systems.
Hexadecimal NumbersHexadecimal Numbers
F111115
E111014
D110113
C110012
B101111
A101010
910019
810008
701117
601106
501015
401004
300113
200102
100011
000000
HexadecimalBinaryDecimal
Hexadecimal NumbersHexadecimal Numbers
�� The notation The notation ‘‘hh’’ is commonly used in is commonly used in
computer impeded system to stand computer impeded system to stand
•• Simply break the binary number into 4Simply break the binary number into 4--bit groups, starting bit groups, starting at the rightat the right--most bit and replace each 4most bit and replace each 4--bit group with the bit group with the equivalent hex symbol.equivalent hex symbol.
�� HexHex--toto--Bin ConversionBin Conversion•• Reverse the process (of binReverse the process (of bin--toto--hex) and hex) and replace each hex symbol with its replace each hex symbol with its equivalent four bits.equivalent four bits.
ex: Determine the binary numbers for the following hex ex: Determine the binary numbers for the following hex numbers:numbers:
•• Multiply the decimal values of each hex digits by its Multiply the decimal values of each hex digits by its weight and then take the sum of these products.weight and then take the sum of these products.
ex: Convert the following hex numbers to decimal:ex: Convert the following hex numbers to decimal:
�� Like the hex, the Like the hex, the ““octoct””provides a convenient provides a convenient way to express binary way to express binary numbers and codes, numbers and codes, but not commonly but not commonly used. used.
�� It uses 8 digits: 0It uses 8 digits: 0--7 as 7 as in the table:in the table:
Octal NumbersOctal Numbers
�� BinBin--toto--Oct ConversionOct Conversion(a) 101110101(a) 101110101 (b) 1011011001 (b) 1011011001 Grouped into 3 digits and write the equivalent octal numberGrouped into 3 digits and write the equivalent octal number
Binary AdditionBinary Addition�� The four basic rules for adding binary The four basic rules for adding binary
digits are as follows:digits are as follows:
•• 0+0=0+0= 00 �� sum of 0 with a carry of 0sum of 0 with a carry of 0
•• 0+1=0+1= 11 �� sum of 1 with a carry of 0sum of 1 with a carry of 0
•• 1+0=1+0= 11 �� sum of 1 with a carry of 0sum of 1 with a carry of 0
•• 1+1=1+1= 1100 �� sum of 0 with a carry of 1sum of 0 with a carry of 1
11 3+11 +3110 6
111 7+ 11 +31010 10
110 6+100 +41010 10
Binary SubtractionBinary Subtraction�� The four basic rules for subtracting The four basic rules for subtracting
binary digits are as follows:binary digits are as follows:
•• 00-- 0 = 0 = 00
•• 11-- 1 = 1 = 00
•• 11-- 0 = 0 = 11
•• 1010-- 1 = 1 = 11 ; 0; 0--1 with a borrow of 11 with a borrow of 1
11 3-01 -1
10 2
11 3-10 -2
01 1
101 5-011 -3
010 2
Binary MultiplicationBinary Multiplication�� The four basic rules for multiplying digits are as The four basic rules for multiplying digits are as follows:follows:
�� Multiplication is performed with binary numbers Multiplication is performed with binary numbers in the same manner as with decimal numbers.in the same manner as with decimal numbers.
•• It involves forming partial products, shifting It involves forming partial products, shifting each successive partial product left one place, each successive partial product left one place, and then adding all the partial products.and then adding all the partial products.
11x11
11+111001
101x111
101101
+101100011
Binary DivisionBinary Division
�� Division in binary follows the same Division in binary follows the same
procedure as division in decimal.procedure as division in decimal.
1011 110
11000
1110 110
1010 1000
11’’s and 2s and 2’’s Complementss Complements�� Negative numbers are normally presented in 1Negative numbers are normally presented in 1’’s or 2s or 2’’s s
complementcomplement..
�� The method of 2The method of 2’’s complement arithmetic s complement arithmetic is commonly is commonly used in computerused in computer systemssystems to handle negative numbersto handle negative numbersmore than 1more than 1’’s complements complement..
Diminished Radix complement 11’’ss
Given a number N in base r having n digits , the (r-1) ’s
complement of N is defined as (r n-1)-N.
Radix Complement: 2 ’’ss
The r’s complement of an n-digit number N in base r is defined as
(rn-N) for N ≠0 and as 0 for N=0
To find the To find the 11’’s complements complement for a given binary numberfor a given binary number::
�� ComplementComplement every every bit in bit in thethe number the number the
result is result is 11’’s complement s complement
ex: find 1ex: find 1’’s complement of 11100101s complement of 1110010122
001100111100000011’’ s complements complement
1100110000111111BinaryBinary
Add 1 to the Add 1 to the 11’’s complements complement to get the to get the 22’’s complement.s complement.