CHAPTER-2 Fundamentals of Digital Logic

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 © 2005 Pearson Education, Inc. All rights reserved.

The 7400 series TTL integrated circuits

From Essentials of Computer Architecture by Douglas E. Comer. ISBN © 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.

Sequential circuits They are logic circuits whose output depend upon past output states. Flips-Flops (or Bistables) are the basic Sequential Logic Elements.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 © 2005 Pearson Education, Inc. All rights reserved.

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 2 N - 1

From Essentials of Computer Architecture by Douglas E. Comer. ISBN © 2005 Pearson Education, Inc. All rights reserved.

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 2 n 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 © 2005 Pearson Education, Inc. All rights reserved.

Logic symbol for 2-line-to-4-line demultiplexer

2-line-to-4-line De-multiplexer

De-multiplexer Function Table D S1S0 Y0 Y1 Y2 Y3 D 0 0 D 000 D D 00 D D0 D D

From Essentials of Computer Architecture by Douglas E. Comer. ISBN © 2005 Pearson Education, Inc. All rights reserved.

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 © 2005 Pearson Education, Inc. All rights reserved.