UNIT – I
Number Systems
P Suresh Babu,
VNRVJIET
2
Why Binary System?
• Computers are made of a series of switches
• Each switch has two states: ON or OFF
• Each state can be represented by a number – 1
for “ON” and 0 for “OFF”
3
Converting Base-2 to Base-10
(1 0 1 1)
2
0
ON
OFF
ON
OFF
ON
Exponent:
Calculation: 0 0 2 1
16+ + + + =
(19)10
4
• Number systems include Decimal, Binary,
Octal and Hexadecimal.
• Each system have four number base
Number System Base Symbol
Binary Base- 2 B
Octal Base- 8 O
Decimal Base- 10 D
Hexadecimal Base- 16 H
5
1.Decimal Number System
• The Decimal Number System uses base 10. It
includes the digits {0, 1,2,…, 9}. The weighted
values for each position are:
10^4 10^3 10^2 10^1 10^0 10^-1 10^-2 10^-3
10000 1000 100 10 1 0.1 0.01 0.001
Base
Right of decimal point
left of the decimal point
6
• Each digit appearing to the left of the decimal
point represents a value between zero and nine
times power of ten represented by its position in
the number.
• Digits appearing to the right of the decimal point
represent a value between zero and nine times an
increasing negative power of ten.
• Ex: the value 725.194 is represented in expansion
form as follows:
• 7 * 10^2 + 2 * 10^1 + 5 * 10^0 + 1 * 10^-1 + 9 *
10^-2 + 4 * 10^-3
• =7 * 100 + 2 * 10 + 5 * 1 + 1 * 0.1 + 9 * 0.01 + 4 *
0.001
• =700 + 20 + 5 + 0.1 + 0.09 + 0.004
• =725.194
7
The Binary Number System
• Most modern computer system using binary logic. The
computer represents values(0,1) using two voltage levels
(usually 0V for logic 0 and either +3.3 V or +5V for logic
1).
• The Binary Number System uses base 2 includes only the
digits 0 and 1
• The weighted values for each position are :
2^5 2^4 2^3 2^2 2^1 2^0 2^-1 2^-2
32 16 8 4 2 1 0.5 0.25
Base
8
1.3 Number Base Conversion
• Binary to Decimal: Multiply each digit by its
weighted position, and add each of the weighted
values together or use expansion formdirectly.
Ex: The binary value 1100 1010 represents :
• 1*2^7 + 1*2^6 + 0*2^5 + 0*2^4 + 1*2^3 + 0*2^2 +
1*2^1 + 0*2^0 =
• 1 * 128 + 1 * 64 + 0 * 32 + 0 * 16 + 1 * 8 + 0 * 4 + 1 *
2 + 0 * 1 =
• 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0 =202
9
• Decimal to Binary
There are two methods, that may be used to convert
from integer number in decimal form to binary form:
I. Repeated Division By 2
• For this method, divide the decimal number by 2,
• If the remainder is 0, on the right side write down a 0.
• If the remainder is 1, write down a 1.
• When performing the division, the remainders which
will represent the binary equivalent of the decimal
number are written beginning at the least significant
digit (right) and each new digit is written to more
significant digit (the left) of the previous digit.
10
• Example: convert the number 333 to binary.
Division Quotient Remainder Binary
333/2 166 1 1
166/2 83 0 01
83/2 41 1 101
41/2 20 1 1101
20/2 10 0 01101
10/2 5 0 001101
5/2 2 1 1001101
2/2 1 0 01001101
1/2 0 1 101001101
11
Octal Number System
• Computer scientists are often looking for
shortcuts to do things
• One of the ways in which we can represent
binary numbers is to use their octal
equivalents instead
• This is especially helpful when we have to do
fairly complicated tasks using numbers
12
• The octal numbering system includes eight base digits
(0-7)
• After 7, the next placeholder to the right begins with
a “1”
• 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13 ...
13
Decimal to Octal: Transform (44978)10 to Octal
• .
Division Quotient Remainder Binary
44978 / 8 5622 2 2
5622 / 8 702 6 62
702/8 87 6 662
87/8 10 7 7662
10/8 1 2 27662
1/8 0 1 127662
14
Exercise
• Fill in the blanks.
Decimal Binary Hexadecimal Octal
1101.0112
10101.112
245.62510
70310
A8516
15
•Answers
Decimal Binary Hexadecimal Octal
13.37510 1101.0112 D.616 15.38
21.7510 10101.112 15.C16 25.68
245.62510 11110101.1012 F5.A16 365.58
70310 10101111112 2BF16 12778
269310 1010100001012 A8516 52058
• SIGNED BINARY NUMBERS
• BINARY CODES
• BINARY LOGIC
Binary Addition
• Column Addition
1 0 1
1
1
1
1
1
1
1 0
+
0
0
0
0 1 1
1
≥ (2)10
1
1
1
1
1
1
= 61
= 23
= 84
Binary Subtraction
• Borrow a “Base” when needed
0 0 1
1
1
0
1
1
1
1 0
−
0
1
0
1 1 1
0
= (10)2
2
2
2 2
1
0
0
0
1
= 77
= 23
= 54
Binary Multiplication
• Bit by bit
0
1 1 1 1
0
1 1 0
0
0 0 0 0
0
1 1 1 1
0
1 1 1 1
0 0 0
0
0
0
1
1
0
1
1
1 0
x
Complements
• There are two types of complements for each base-r system: the radix complement
and diminished radix complement.
• Diminished Radix Complement - (r-1)’s Complement
– Given a number N in base r having n digits, the (r–
1)’s complement of N is defined as:
(rn –1) – N
• Example for 6-digit decimal numbers:
– 9’s complement is (rn – 1)–N = (106–1)–N = 999999–
N
– 9’s complement of 546700 is 999999–546700 =
453299
• Example for 7-digit binary numbers:
– 1’s complement is (rn – 1) – N = (27–1)–N =
Complements
• 1’s Complement (Diminished Radix
Complement)
– All ‘0’s become ‘1’s
– All ‘1’s become ‘0’s
Example (10110000)2
 (01001111)2
If you add a number and its 1’s complement …
1 0 1 1 0 0 0 0
+ 0 1 0 0 1 1 1 1
1 1 1 1 1 1 1 1
Signed Binary Numbers
• To represent negative integers, we need a
notation for negative values.
• It is customary to represent the sign with a bit
placed in the leftmost position of the number
since binary digits.
• The convention is to make the sign bit 0 for
positive and 1 for negative.
• Example:
Signed Binary Numbers
• Arithmetic addition
– The addition of two numbers in the signed-magnitude system follows the rules
of ordinary arithmetic. If the signs are the same, we add the two magnitudes
and give the sum the common sign. If the signs are different, we subtract the
smaller magnitude from the larger and give the difference the sign if the larger
magnitude.
– The addition of two signed binary numbers with negative numbers
represented in signed-2's-complement form is obtained from the addition of
the two numbers, including their sign bits.
– A carry out of the sign-bit position is discarded.
• Example:
Signed Binary Numbers
• Arithmetic Subtraction
– In 2’s-complement form:
• Example:
1. Take the 2’s complement of the subtrahend (including the sign bit)
and add it to the minuend (including sign bit).
2. A carry out of sign-bit position is discarded.
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
A B A B
A B A B
      
      
( 6)  ( 13) (11111010  11110011)
(11111010 + 00001101)
00000111 (+ 7)
Binary Codes
• BCD Code
– A number with k decimal
digits will require 4k bits in
BCD.
– Decimal 396 is
represented in BCD with
12bits as 0011 1001 0110,
with each group of 4 bits
representing one decimal
digit.
– A decimal number in BCD
is the same as its
Binary Codes
• Example:
– Consider decimal 185 and its corresponding value
in BCD and binary:
• BCD addition
Binary Codes
• Gray Code
– The advantage is that
only bit in the code
group changes in going
from one number to the
next.
• Error detection.
• Representation of analog data.
• Low power design.
000 001
010
100
110 111
101
011
1-1 and onto!!
Binary Codes
• ASCII Character Code
ASCII Character Codes
• American Standard Code for Information Interchange
(Refer to Table 1.7)
• A popular code used to represent information sent as
character-based data.
• It uses 7-bits to represent:
– 94 Graphic printing characters.
– 34 Non-printing characters.
• Some non-printing characters are used for text
format (e.g. BS = Backspace, CR = carriage return).
• Other non-printing characters are used for record
marking and flow control (e.g. STX and ETX start and
end text areas).
ASCII Properties
• ASCII has some interesting properties:
– Digits 0 to 9 span Hexadecimal values 3016 to 3916
– Upper case A-Z span 4116 to 5A16
– Lower case a-z span 6116 to 7A16
• Lower to upper case translation (and vice versa) occurs by flipping bit 6.
Binary Logic
• Definition of Binary Logic
– Binary logic consists of binary variables and a set of logical operations.
– The variables are designated by letters of the alphabet, such as A, B, C, x, y, z,
etc, with each variable having two and only two distinct possible values: 1 and
0,
– Three basic logical operations: AND, OR, and NOT.
Binary Logic
• Truth Tables:
x y z
0 0 0
0 1 0
1 0 0
1 1 1
x y z
0 0 0
0 1 1
1 0 1
1 1 1
x z
0 1
1 0
AND OR NOT
x
y z x
y z
z = x • y = x y z = x + y z = x = x’
x z
• Boolean
Expressions:
• Logic Gates:
Switching Circuits
AND OR
Binary Logic
• Logic gates
– Graphic Symbols and Input-Output Signals for
Logic gates:
Fig. 1.4 Symbols for digital logic circuits
Fig. 1.5 Input-Output signals for gates
Binary Logic
• Logic gates
– Graphic Symbols and Input-Output Signals for
Logic gates:
Fig. 1.6 Gates with multiple inputs

More Related Content

PPT
digitalelectronics.ppt
PDF
Digital Logic
PDF
Finite word length effects
PDF
Digital Electronics – Unit I.pdf
PPT
lect1.ppt
PPT
Number system and codes
PPT
Digital fundamendals r001a
digitalelectronics.ppt
Digital Logic
Finite word length effects
Digital Electronics – Unit I.pdf
lect1.ppt
Number system and codes
Digital fundamendals r001a

Similar to Number Systems.ppt (20)

PPTX
Unit-1 Digital Design and Binary Numbers:
PDF
Standard 9th Number System Power point presentation
PPTX
21EC201– Digital Principles and system design.pptx
PPTX
Eln PPT module on electrical and electronics
PPT
Number_Systems (2).ppt
PPT
2. Computer_Organization_unit_ 1_win.ppt
PDF
Module 1 Digital Logic Design .pptx.pdf
PPTX
Digital Electronics Introduction Prerequisite
PPTX
1.Digital Electronics overview & Number Systems.pptx
PPTX
data representation
PPTX
digital-electronics lecture Ch 1and 2 -1.pptx
PDF
Digital Logic Computer Design lecture notes
PPT
An introduction to the different number systems
PPT
Number Systems and its effectiveness .ppt
PPT
Number_Systems_Number base conversions.ppt
PPT
Number_Systems decimal, binary, octal, and hexadecimal
PPT
Number_Systems _binary_octal_hex_dec.ppt
PPT
DLD_Lecture_notes2.ppt
PPT
De numbers systems vk ppt
PDF
Representasi Data, SISTEM BILANGAN, KODE BILANGAN
Unit-1 Digital Design and Binary Numbers:
Standard 9th Number System Power point presentation
21EC201– Digital Principles and system design.pptx
Eln PPT module on electrical and electronics
Number_Systems (2).ppt
2. Computer_Organization_unit_ 1_win.ppt
Module 1 Digital Logic Design .pptx.pdf
Digital Electronics Introduction Prerequisite
1.Digital Electronics overview & Number Systems.pptx
data representation
digital-electronics lecture Ch 1and 2 -1.pptx
Digital Logic Computer Design lecture notes
An introduction to the different number systems
Number Systems and its effectiveness .ppt
Number_Systems_Number base conversions.ppt
Number_Systems decimal, binary, octal, and hexadecimal
Number_Systems _binary_octal_hex_dec.ppt
DLD_Lecture_notes2.ppt
De numbers systems vk ppt
Representasi Data, SISTEM BILANGAN, KODE BILANGAN
Ad

Recently uploaded (20)

PPTX
Virtual and Augmented Reality in Current Scenario
PDF
MBA _Common_ 2nd year Syllabus _2021-22_.pdf
PPTX
Unit 4 Computer Architecture Multicore Processor.pptx
PDF
Empowerment Technology for Senior High School Guide
PDF
FOISHS ANNUAL IMPLEMENTATION PLAN 2025.pdf
PPTX
Chinmaya Tiranga Azadi Quiz (Class 7-8 )
PDF
1.3 FINAL REVISED K-10 PE and Health CG 2023 Grades 4-10 (1).pdf
PDF
medical_surgical_nursing_10th_edition_ignatavicius_TEST_BANK_pdf.pdf
PDF
FORM 1 BIOLOGY MIND MAPS and their schemes
PDF
Τίμαιος είναι φιλοσοφικός διάλογος του Πλάτωνα
PDF
BP 704 T. NOVEL DRUG DELIVERY SYSTEMS (UNIT 2).pdf
PPTX
B.Sc. DS Unit 2 Software Engineering.pptx
PDF
OBE - B.A.(HON'S) IN INTERIOR ARCHITECTURE -Ar.MOHIUDDIN.pdf
PPTX
20th Century Theater, Methods, History.pptx
PDF
David L Page_DCI Research Study Journey_how Methodology can inform one's prac...
PPTX
Onco Emergencies - Spinal cord compression Superior vena cava syndrome Febr...
PDF
Uderstanding digital marketing and marketing stratergie for engaging the digi...
PDF
Environmental Education MCQ BD2EE - Share Source.pdf
PPTX
History, Philosophy and sociology of education (1).pptx
PDF
AI-driven educational solutions for real-life interventions in the Philippine...
Virtual and Augmented Reality in Current Scenario
MBA _Common_ 2nd year Syllabus _2021-22_.pdf
Unit 4 Computer Architecture Multicore Processor.pptx
Empowerment Technology for Senior High School Guide
FOISHS ANNUAL IMPLEMENTATION PLAN 2025.pdf
Chinmaya Tiranga Azadi Quiz (Class 7-8 )
1.3 FINAL REVISED K-10 PE and Health CG 2023 Grades 4-10 (1).pdf
medical_surgical_nursing_10th_edition_ignatavicius_TEST_BANK_pdf.pdf
FORM 1 BIOLOGY MIND MAPS and their schemes
Τίμαιος είναι φιλοσοφικός διάλογος του Πλάτωνα
BP 704 T. NOVEL DRUG DELIVERY SYSTEMS (UNIT 2).pdf
B.Sc. DS Unit 2 Software Engineering.pptx
OBE - B.A.(HON'S) IN INTERIOR ARCHITECTURE -Ar.MOHIUDDIN.pdf
20th Century Theater, Methods, History.pptx
David L Page_DCI Research Study Journey_how Methodology can inform one's prac...
Onco Emergencies - Spinal cord compression Superior vena cava syndrome Febr...
Uderstanding digital marketing and marketing stratergie for engaging the digi...
Environmental Education MCQ BD2EE - Share Source.pdf
History, Philosophy and sociology of education (1).pptx
AI-driven educational solutions for real-life interventions in the Philippine...
Ad

Number Systems.ppt

  • 1. UNIT – I Number Systems P Suresh Babu, VNRVJIET
  • 2. 2 Why Binary System? • Computers are made of a series of switches • Each switch has two states: ON or OFF • Each state can be represented by a number – 1 for “ON” and 0 for “OFF”
  • 3. 3 Converting Base-2 to Base-10 (1 0 1 1) 2 0 ON OFF ON OFF ON Exponent: Calculation: 0 0 2 1 16+ + + + = (19)10
  • 4. 4 • Number systems include Decimal, Binary, Octal and Hexadecimal. • Each system have four number base Number System Base Symbol Binary Base- 2 B Octal Base- 8 O Decimal Base- 10 D Hexadecimal Base- 16 H
  • 5. 5 1.Decimal Number System • The Decimal Number System uses base 10. It includes the digits {0, 1,2,…, 9}. The weighted values for each position are: 10^4 10^3 10^2 10^1 10^0 10^-1 10^-2 10^-3 10000 1000 100 10 1 0.1 0.01 0.001 Base Right of decimal point left of the decimal point
  • 6. 6 • Each digit appearing to the left of the decimal point represents a value between zero and nine times power of ten represented by its position in the number. • Digits appearing to the right of the decimal point represent a value between zero and nine times an increasing negative power of ten. • Ex: the value 725.194 is represented in expansion form as follows: • 7 * 10^2 + 2 * 10^1 + 5 * 10^0 + 1 * 10^-1 + 9 * 10^-2 + 4 * 10^-3 • =7 * 100 + 2 * 10 + 5 * 1 + 1 * 0.1 + 9 * 0.01 + 4 * 0.001 • =700 + 20 + 5 + 0.1 + 0.09 + 0.004 • =725.194
  • 7. 7 The Binary Number System • Most modern computer system using binary logic. The computer represents values(0,1) using two voltage levels (usually 0V for logic 0 and either +3.3 V or +5V for logic 1). • The Binary Number System uses base 2 includes only the digits 0 and 1 • The weighted values for each position are : 2^5 2^4 2^3 2^2 2^1 2^0 2^-1 2^-2 32 16 8 4 2 1 0.5 0.25 Base
  • 8. 8 1.3 Number Base Conversion • Binary to Decimal: Multiply each digit by its weighted position, and add each of the weighted values together or use expansion formdirectly. Ex: The binary value 1100 1010 represents : • 1*2^7 + 1*2^6 + 0*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = • 1 * 128 + 1 * 64 + 0 * 32 + 0 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 0 * 1 = • 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0 =202
  • 9. 9 • Decimal to Binary There are two methods, that may be used to convert from integer number in decimal form to binary form: I. Repeated Division By 2 • For this method, divide the decimal number by 2, • If the remainder is 0, on the right side write down a 0. • If the remainder is 1, write down a 1. • When performing the division, the remainders which will represent the binary equivalent of the decimal number are written beginning at the least significant digit (right) and each new digit is written to more significant digit (the left) of the previous digit.
  • 10. 10 • Example: convert the number 333 to binary. Division Quotient Remainder Binary 333/2 166 1 1 166/2 83 0 01 83/2 41 1 101 41/2 20 1 1101 20/2 10 0 01101 10/2 5 0 001101 5/2 2 1 1001101 2/2 1 0 01001101 1/2 0 1 101001101
  • 11. 11 Octal Number System • Computer scientists are often looking for shortcuts to do things • One of the ways in which we can represent binary numbers is to use their octal equivalents instead • This is especially helpful when we have to do fairly complicated tasks using numbers
  • 12. 12 • The octal numbering system includes eight base digits (0-7) • After 7, the next placeholder to the right begins with a “1” • 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13 ...
  • 13. 13 Decimal to Octal: Transform (44978)10 to Octal • . Division Quotient Remainder Binary 44978 / 8 5622 2 2 5622 / 8 702 6 62 702/8 87 6 662 87/8 10 7 7662 10/8 1 2 27662 1/8 0 1 127662
  • 14. 14 Exercise • Fill in the blanks. Decimal Binary Hexadecimal Octal 1101.0112 10101.112 245.62510 70310 A8516
  • 15. 15 •Answers Decimal Binary Hexadecimal Octal 13.37510 1101.0112 D.616 15.38 21.7510 10101.112 15.C16 25.68 245.62510 11110101.1012 F5.A16 365.58 70310 10101111112 2BF16 12778 269310 1010100001012 A8516 52058
  • 16. • SIGNED BINARY NUMBERS • BINARY CODES • BINARY LOGIC
  • 17. Binary Addition • Column Addition 1 0 1 1 1 1 1 1 1 1 0 + 0 0 0 0 1 1 1 ≥ (2)10 1 1 1 1 1 1 = 61 = 23 = 84
  • 18. Binary Subtraction • Borrow a “Base” when needed 0 0 1 1 1 0 1 1 1 1 0 − 0 1 0 1 1 1 0 = (10)2 2 2 2 2 1 0 0 0 1 = 77 = 23 = 54
  • 19. Binary Multiplication • Bit by bit 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 x
  • 20. Complements • There are two types of complements for each base-r system: the radix complement and diminished radix complement. • Diminished Radix Complement - (r-1)’s Complement – Given a number N in base r having n digits, the (r– 1)’s complement of N is defined as: (rn –1) – N • Example for 6-digit decimal numbers: – 9’s complement is (rn – 1)–N = (106–1)–N = 999999– N – 9’s complement of 546700 is 999999–546700 = 453299 • Example for 7-digit binary numbers: – 1’s complement is (rn – 1) – N = (27–1)–N =
  • 21. Complements • 1’s Complement (Diminished Radix Complement) – All ‘0’s become ‘1’s – All ‘1’s become ‘0’s Example (10110000)2  (01001111)2 If you add a number and its 1’s complement … 1 0 1 1 0 0 0 0 + 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1
  • 22. Signed Binary Numbers • To represent negative integers, we need a notation for negative values. • It is customary to represent the sign with a bit placed in the leftmost position of the number since binary digits. • The convention is to make the sign bit 0 for positive and 1 for negative. • Example:
  • 23. Signed Binary Numbers • Arithmetic addition – The addition of two numbers in the signed-magnitude system follows the rules of ordinary arithmetic. If the signs are the same, we add the two magnitudes and give the sum the common sign. If the signs are different, we subtract the smaller magnitude from the larger and give the difference the sign if the larger magnitude. – The addition of two signed binary numbers with negative numbers represented in signed-2's-complement form is obtained from the addition of the two numbers, including their sign bits. – A carry out of the sign-bit position is discarded. • Example:
  • 24. Signed Binary Numbers • Arithmetic Subtraction – In 2’s-complement form: • Example: 1. Take the 2’s complement of the subtrahend (including the sign bit) and add it to the minuend (including sign bit). 2. A carry out of sign-bit position is discarded. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) A B A B A B A B               ( 6)  ( 13) (11111010  11110011) (11111010 + 00001101) 00000111 (+ 7)
  • 25. Binary Codes • BCD Code – A number with k decimal digits will require 4k bits in BCD. – Decimal 396 is represented in BCD with 12bits as 0011 1001 0110, with each group of 4 bits representing one decimal digit. – A decimal number in BCD is the same as its
  • 26. Binary Codes • Example: – Consider decimal 185 and its corresponding value in BCD and binary: • BCD addition
  • 27. Binary Codes • Gray Code – The advantage is that only bit in the code group changes in going from one number to the next. • Error detection. • Representation of analog data. • Low power design. 000 001 010 100 110 111 101 011 1-1 and onto!!
  • 28. Binary Codes • ASCII Character Code
  • 29. ASCII Character Codes • American Standard Code for Information Interchange (Refer to Table 1.7) • A popular code used to represent information sent as character-based data. • It uses 7-bits to represent: – 94 Graphic printing characters. – 34 Non-printing characters. • Some non-printing characters are used for text format (e.g. BS = Backspace, CR = carriage return). • Other non-printing characters are used for record marking and flow control (e.g. STX and ETX start and end text areas).
  • 30. ASCII Properties • ASCII has some interesting properties: – Digits 0 to 9 span Hexadecimal values 3016 to 3916 – Upper case A-Z span 4116 to 5A16 – Lower case a-z span 6116 to 7A16 • Lower to upper case translation (and vice versa) occurs by flipping bit 6.
  • 31. Binary Logic • Definition of Binary Logic – Binary logic consists of binary variables and a set of logical operations. – The variables are designated by letters of the alphabet, such as A, B, C, x, y, z, etc, with each variable having two and only two distinct possible values: 1 and 0, – Three basic logical operations: AND, OR, and NOT.
  • 32. Binary Logic • Truth Tables: x y z 0 0 0 0 1 0 1 0 0 1 1 1 x y z 0 0 0 0 1 1 1 0 1 1 1 1 x z 0 1 1 0 AND OR NOT x y z x y z z = x • y = x y z = x + y z = x = x’ x z • Boolean Expressions: • Logic Gates:
  • 34. Binary Logic • Logic gates – Graphic Symbols and Input-Output Signals for Logic gates: Fig. 1.4 Symbols for digital logic circuits Fig. 1.5 Input-Output signals for gates
  • 35. Binary Logic • Logic gates – Graphic Symbols and Input-Output Signals for Logic gates: Fig. 1.6 Gates with multiple inputs