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Fundamentals of Digital Logic
CHAPTER-2
Digital Logic
 Digital electronic circuits are used to build computer
hardware as well as other products (digital
hardware)
 These circuits are fabricated on silicon wafers which
form the chips.
 Chips have from tens to millions of transistors
What is a transistor?
 Transistor is a semiconductor device used to
control flow of electric current.
 It has three connections to an external circuit.
 The transistor provides amplification of a signal.
 A small current(input)through one pair of terminal
causes a large current through the other pair
(output).
Working of a Transistor
 Transistor is used as a switch with a binary
function: five volts – ON, less than
five volts – OFF
0 volts = on
5 volts = off
 In a digital circuit, a signal is represented in one of
two states or logic level.
0 = false = no
1 = true = yes
Working of a transistor
 B - Base
 C – Collector
 E - Emitter
Logic Gates
 Transistors are used to create logic gates.
 logic gates are blocks of hardware that produce
signals of 0 or 1.
 There are seven basic logic gates: AND, OR, XOR,
NOT, NAND, NOR, and XNOR
How are digital circuits built ?
 Operations of logic gates are described using Boolean
Algebra.
 And , or and not are Boolean functions.
 Transistors construct circuits which implement
Boolean functions.
 Input and out put relationship of the binary variables
can be represented as truth tables.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
The 7400 series TTL integrated circuits
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
Combinatorial or combinational circuits:
 They consist of basic Boolean operations (AND, OR,




NOT), and the output represents a Boolean function.
They are logic circuits whose output depends upon the
presently given input only.
They don't have any memory.
They are used to perform Boolean algebra on the
present input and stored data.
They do not have any clock.
Sequential circuits
 They are logic circuits whose output depend upon
past output states.
 Flips-Flops (or Bistables) are the basic Sequential
Logic Elements.
 Sequential circuits have state, which means
sequential circuits have memory.
 State is updated based on a clock.
Flip-flop
Flip-flop: It is a state maintaining mechanism.
It is a binary cell capable of storing one bit of information. It has
only one out put
 A flip-flop maintains its state until directed by a clock pulse .
Clock: It allows the hardware to operate without requiring the
input to change.
It emits alternating sequence of 0 and 1.
NO. of times the clock cycles through 1 to 0 in a sec is its speed.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
Binary counter
 A register which goes through a predetermined




sequence of states when input is applied is a counter.
A counter accumulates numeric total, it has multiple
outputs
When it reaches the maximum limit the counter is
reset to zero, indicating an overflow.
A counter which follows binary sequence is called a
binary counter.
N-bit binary counter is a register of n flip flops and
sequence of states from 0 to 2N - 1
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
State diagram of a 3-bit binary counter.
 It requires 3 flip flops and the
sequence is 8.
 State transition occurs every time
the clock pulse occurs.
 It takes input from the clock pulse
and output depends on internal
state (outputs are taken off each
flip-flop in the counter
Multiplexer & de-multiplexer
Multiplexer:
 It is a digital circuit with multiple signal inputs,
which gives a single output.
 The out put is selected by a only one addressing
input.
De-multiplexer:
 It is a digital circuit that takes a single data input,
and gives multiple outputs
 The addressing inputs select which one of the
outputs will receive the input signal one or more
address inputs
De-multiplexer
 n-bit binary number and produces an output on one




of 2n output lines.
That means two, three, or four addressing lines, demultiplex up to four, eight, or sixteen multiplexed
signals respectively.
1-to-2 line decoder/de-multiplexer
2-to-4 line decoder/de-multiplexer
3-to-8 line decoder/de-multiplexer
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
Logic symbol for 2-line-to-4-line
demultiplexer
2-line-to-4-line De-multiplexer
De-multiplexer Function Table
D
S1
S0
Y0
Y1
Y2
Y3
D
0
0
D
0
0
0
D
0
1
0
D
0
0
D
1
0
0
0
D
0
D
1
1
0
0
0
D
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
Starting a Sequence
 To start the circuit connect another input
(e.g. push button)to the counter reset.
 When the user pushes the button the counter resets to zero.
 Counter’s output becomes 000
 When the de-multiplexer receives the input of all zero’s it turns on
its first output.
Replication in hardware
 Hardware engineers prefer replication to iteration.
 Hence the need for minimization of the circuits.
 Rule is to optimize the Boolean formula’s forming the
circuits.
 Ex : not (not x) = x, a pair of directly connected inverters
are removed from the circuit without affecting the result.
 x nor (not x) , nor gate and inverter used together will
always give a zero.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights