1. DIGITAL ELECTRONICS CIRCUIT
PREPARED BY
MS.SHANKHA MITRA SUNANI
ASSISTANT PROF.IN THE
DEPARTMENT OF ETC
P.M.E.C GOVT.ENGINEERING
COLLEGE BERHAMPUR
2. CONTENT
MODULE – I
Number System:
• Introduction to various number systems and their Conversion
• Arithmetic Operation using 1’s and 2`s Compliments,
• Signed Binary number
• Introduction to Binary codes and their applications.
• Boolean algebra and identities, Complete Logic set
• logic gates and truth tables
• Universal logic gates, NAND and NOR Logic Implementations
• Algebraic Reductionand realization using logic gates
• Canonical Logic Forms, Extracting Canonical Forms
• K-Maps: Two, Three and Four variable K-maps,
MODULE – II
COMBINATIONAL LOGIC DESIGN
• Concept of Digital Components
• HALF ADDER,FULL ADDER,HALF SUBSTRACTOR,FULL SUBSTRACTOR
• BINARY MULTIPLIER,MAGNITUDE COMPARATOR
• Line Decoder, encoders
• Multiplexers and De-multiplexers
3. Synchronous Sequential logic Design
• Latches (SR, D)
• Flip-Flops
• characteristics equation and state diagram of each FFs
• Conversion of Flip-Flops
• Analysis of Clocked Sequential circuits and Mealy and Moore Models of Finite State
Machines
COUNTERS
• Binary Counters :Introduction
• Principle and design of synchronous counters
• Principle and design of asynchronous counters
• Design of MOD-N counters
• Ring counters. Decade counters
• State Diagram of binary counters
MODULE – III
Shift resistors
• Principle of 4-bit shift resistors
• Shifting principle, Timing Diagram
• SISO, SIPO ,PISO and PIPO resistors.
4. Memory and Programmable Logic
• Types of Memories, Memory Decoding, error detection and correction),
• RAM and ROMs. Programmable Logic Array, Programmable Array Logic, Sequential
Programmable Devices.
IC Logic Families
• Properties DTL, RTL, TTL, I2L and CMOS and its gate level implementation
• A/D converters and D/A converters
5. The general idea is to introduce you to the different number systems: Binary, Octal etc.
and how to convert those numbers to/from the decimal number system
How do you convert a binary to decimal?
Convert 11010 to decimal.
•First write the binary number as-
1 1 0 1 0
• now below every digit write the weight of that position as-
1 1 0 1 0
4 3 2 1 0
2 2 2 2 2
• rewrite them in the expanded form as-
1 1 0 1 0
16 8 4 2 1
• then multiply the corresponding values and add the resulting terms
1*16 + 1*8 + 0*4 + 1*2 + 0*1
= 16 + 8 + 0 + 2 + 0
= 26
How to convert a decimal number into binary form?
To convert a decimal number to binary, keep dividing the number by 2 until the quotient
reaches 0 and note all the remainders obtained after every division
6. Convert 73 to binary..
Quotient remainder
• 73/2 = 1 36
• 36/2 = 0 18
• 18/2 = 0 9
• 9/2 = 1 4
• 4/2 = 0 2
• 2/2 = 0 1
• 1/2 = 1 0
• write the remainders in reverse order i.e. from bottom to top. So the binary equivalent of
73 is 1001001.
7. BINARY ADDITION
There are four basic rules for binary addition--
• 0+0= 0
• 0+1 = 1
• 1 +0= 1
• 1 + 1 = 10
• Let's add two binary numbers say- 10011 and 01000. Binary addition is also carried out the same way as you
normally add two numbers
• 10011
• 01000
• --------
• 11011
• BINARY SUBTRACTION
Basic Rules for binary subtraction are-
• 0-0=0
• 1-0 =1
• 1-1 =1
• 10-1 = 1
8. 8
Boolean Algebra
• George Boole 2 November 1815 Lincoln Lincolnshire, England – 8 December 1864 Ballintemple,
Ireland Professor at Queens College, Cork, Ireland.spring of 1847 that he put his ideas into the
pamphlet called Mathematical Analysis of Logic.” from wikipedia.com he developed boolean
algebra.
• Theorems & Proofs
Theorem 1: a+b = b+a, ab=ba (commutative)
Theorem 2: a+bc = (a+b)(a+c) (distributive)
Theorem3 a(b+c) = ab + ac
Theorem 4: a+0=a, a1 = a (identity)
Theorem 5: a+a’=1, a a’= 0 (complement) X + X’ = 1 X · X’ = 0
Associative X+(Y+Z)=(X+Y)+Z
Theorem 6 (Involution Laws):
• For every element a in , (a')' = a
Proof: a is one complement of a'.
The complement of a' is unique
Thus a = (a')'
Theorem 7 (Absorption Law): For every pair a,b in a·(a+b) = a; a + a·b = a.
Proof: a(a+b)
= (a+0)(a+b)
= a+0·b
= a + 0
= a
9. Theorem 8
For every pair a, b in B
a + a’*b = a + b; a*(a’ + b) = a*b
Proof: a + a’*b
= (a + a’)*(a + b)
= (1)*(a + b)
= (a + b)
Theorem 9: De Morgan’s Law
• (X + Y)’ = X’ · Y’
• (XY)’ = X’ + Y’
Simplify
F=X’YZ+X’YZ’+XZ
10. Duals
• What is meant by the dual of a function?
– The dual of a function is obtained by interchanging OR and AND operations
and replacing 1s and 0s with 0s and 1s.
Show that a’b’+ab+a’b = a’+b
Proof 1: a’b’+ab+a’b = a’b’+(a+a’)b
= a’b’ + b
= a’ + b
SIMPLIFY (a’b’+c)(a+b)(b’+ac)’
= (a’b’+c)(a+b)(b(ac)’)
= (a’b’+c)(a+b)b(a’+c’)
= (a’b’+c)b(a’+c’)
= (a’b’b+bc)(a’+c’)
= (0+bc)(a’+c’)
= bc(a’+c’)
= a’bc+bcc’
= a’bc+0
= a’bc
10
11. LOGIC Gates
• The most basic digital devices are called gates.
• Gates got their name from their function of allowing or blocking (gating) the flow
of digital information.
• A gate has one or more inputs and produces an output depending on the input(s).
• A gate is called a combinational circuit.
• Three most important gates are: AND, OR, NOT
12. Exclusive-OR Gate
X Y Z
X
Y
Z
0 0 0
0 1 1
1 0 1
1 1 0
X
Y
Z X Y Z
0 0 1
0 1 0
1 0 0
1 1 1
13. UNIVERSAL GATE
• A universal gate is a gate which can implement any Boolean function without need to use
any other gate type.
• The NAND and NOR gates are universal gates.
• In practice, this is advantageous since NAND and NOR gates are economical and easier to
fabricate and are the basic gates used in all IC digital logic families.
• In fact, an AND gate is typically implemented as a NAND gate followed by an inverter not
the other way around!!
• Likewise, an OR gate is typically implemented as a NOR gate followed by an inverter not
the other way around!!
NAND Gate is a Universal Gate:
To prove that any Boolean function can be implemented using only NAND gates, we will show
that the AND, OR, and NOT operations can be performed using only these gates.
• Implementing an Inverter Using only NAND Gate
• The figure shows two ways in which a NAND gate can be used as an inverter (NOT gate).
• All NAND input pins connect to the input signal A gives an output A’.
14. COUNTER
• Counter is a sequential logic circuit which is count the binary sequence
sequentially.
• Counter is divided in to two types
• Synchronous counter
• Asynchronous counter
• In synchronous counter all the flipflop is triggered by clockpulse
simultaneously
• In asynchronous counter the first flip flop is triggered by clock pulse and the
output of first flip flop is given to second flip flop and so on
• According to counting the sequence fipflop is divided in to two types
• UP COUNTER
• DOWN COUNTER
• In up counter the counter counts in ascending order
• In down counter the counter counts the binary sequence in decending order
• If n= Number of fipflop is used in the counter to design & N= Number of binary
states that counter count then N<=2n
