Digital Systems Are Said to Be Constructed by Using Logic Gates. the Basic Gates Are The

Logic gates

Digital systems are said to be constructed by using logic gates. The basic gates are the AND, OR, NOT gates. The basic operations are described below with the aid of tables in the following, called truth tables.

AND gate

The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high. A dot (.) is used to show the AND operation i.e. A.B. Bear in mind that this dot is sometimes omitted i.e. AB

OR gate

The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high. A plus (+) is used to show the OR operation.

NOT gate

The NOT gate is an electronic circuit that produces an inverted version of the input at its output. It is also known as an inverter. If the input variable is A, the inverted output is known as NOT A. This is also shown as A', or A with a bar over the top, as shown at the outputs.

Another useful gate used in the digital logic circuits is EXOR gate.

EXOR gate

The 'Exclusive-OR' gate is a circuit which will give a high output if either, but not both, of its two inputs are high. An encircled plus sign ( ) is used to show the EOR operation.

** Here also note that a truth table with 'n' inputs has 2n rows ** Simple Binary Adder (Half Adder) ______

A key requirement of digital computers is the ability to use logical functions to perform arithmetic operations. The basis of this is addition; if we can add two binary numbers, we can just as easily subtract them, or get a little fancier and perform multiplication and division. How, then, do we add two binary numbers?

Let's start by adding two binary bits. Since each bit has only two possible values, 0 or 1, there are only four possible combinations of inputs. These four possibilities, and the resulting sums, are:

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10

Whoops! That fourth line indicates that we have to account for two output bits when we add two input bits: the sum and a possible carry. Let's set this up as a truth table with two inputs and two outputs, and see where we can go from there.

INPUTS OUTPUTS A B CARRY SUM Well, this looks familiar, doesn't it? The Carry output 0 0 0 0 is a simple AND function, and the Sum is an Exclusive- 0 1 0 1 OR. Thus, we can use two gates to add these two bits together. The resulting circuit is shown below. 1 0 0 1 1 1 1 0

Fig: Diagram of binary adder Set – Reset (SR) Flip Flop ______

"Flip-flop" is the common name given to two-state devices which offer basic memory for sequential logic operations. Flip-flops are heavily used for digital data storage and transfer and are commonly used in banks called "registers" for the storage of binary numerical data.

The SRFF (Set – Reset Flip Flop) can be constructed of two NOR gates plus feedback as shown in the circuit diagrams below. In this SRFF both set and reset cannot be 1 as it generates an unstable state.

Fig : SR Flipflop

S R Q Q’ 1 0 1 0 0 0 1 0 0 1 0 1

Here looking at the table we see that The output Q still keeps its value unchanged when S is switched from 1 to 0 and it only changes when R is made 1 or Reset. This is how basic memory units work.

Reference : Multiplexer ______

This is a digital circuit with multiple signal inputs, one of which is selected by separate address inputs to be sent to the single output. It's not easy to describe without the logic diagram, but is easy to understand when the diagram is available.

A two-input multiplexer is shown below.

The multiplexer circuit is typically used to combine two or more digital signals onto a single line, by placing them there at different times. Technically, this is known as time-division multiplexing.

Input A is the addressing input, which controls which of the two data inputs, X0 or X1, will be transmitted to the output. If the A input switches back and forth at a frequency more than double the frequency of either digital signal, both signals will be accurately reproduced, and can be separated again by a demultiplexer circuit synchronized to the multiplexer.

This is not as difficult as it may seem at first glance; the telephone network combines multiple audio signals onto a single pair of wires using exactly this technique, and is readily able to separate many telephone conversations so that everyone's voice goes only to the intended recipient. With the growth of the Internet and the World Wide Web, most people have heard about T1 telephone lines. A T1 line can transmit up to 24 individual telephone conversations by multiplexing them in this manner. Demultiplexer ______

The opposite of the multiplexer circuit, logically enough, is the demultiplexer. This circuit takes a single data input and one or more address inputs, and selects which of multiple outputs will receive the input signal. The same circuit can also be used as a decoder, by using the address inputs as a binary number and producing an output signal on the single output that matches the binary address input. In this application, the data input line functions as a circuit enabler — if the circuit is disabled, no output will show activity regardless of the binary input number.

A one-line to two-line decoder/demultiplexer is shown below.

This circuit uses the same AND gates and the same addressing scheme as the two-input multiplexer circuit shown in these pages. The basic difference is that it is the inputs that are combined and the outputs that are separate. By making this change, we get a circuit that is the inverse of the two-input multiplexer.