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Chapter-2
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
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).
Transistor is used as a switch with a binary function: five volts – ON, less than
five volts – OFF 5 volts = on 0 volts = off In a digital circuit, a signal is
represented in one of two states or logic level.
0 = false = no 1 = true = yes
B - Base C – Collector E - Emitter
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
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 reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
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.
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: 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 reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
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 reserved.
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: 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
n-bit binary number and produces an output on one of 2n output lines.
That means two, three, or four addressing lines, de-multiplex 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 reserved.
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 reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
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 reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
