LOGIC GATES AND LOGIC CIRCUITS A logic gate is an elementary building block of a Digital Circuit. Most logic gates have two inputs and one output.

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1 LOGIC GATES AND LOGIC CIRCUITS A logic gate is an elementary building block of a Digital Circuit. Most logic gates have two inputs and one output. At any given moment, every terminal is in one of the two binary conditions low (0) or high (1), represented by different voltage levels..

2 LOGIC GATES The logic state of a terminal can, and generally does, change often, as the circuit processes data. In most logic gates, the low state is approximately zero volts (0 V), while the high state is approximately five volts positive (+5 V). There are seven basic logic gates: AND, OR, XOR, NOT, NAND, NOR, and XNOR

3 The AND gate This is a logical "and" operator. The output is "1 when both inputs are "1, Otherwise, the output is "0. The following illustration and table show the circuit symbol and logic combinations (truth table) for an AND gate. 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

4 The OR gate This is a logical inclusive "or operator. The output is 1" if either or both of the inputs are 1. If both inputs are 0" then the output is 0. The circuit symbol and logic combinations (truth table) for an OR gate are as: A plus (+) is used to show the OR operation.

5 The XOR ( exclusive-or ) gate This is the logical "either/or. operator. The output is "1" if either, but not both, of the inputs are "1." The output is "0" if both inputs are "0" or if both inputs are "1." Another way of looking at this circuit is to observe that the output is 1 if the inputs are different, but 0 if the inputs are the same. It uses an encircled plus sign is used to show the XOR operation.

6 The circuit symbol and logic combinations (truth table) for an XOR gate are as:

7 The NOT gate This is a logical inverter. The NOT gate has only one input. It reverses the logic state. When the input is 1, the output is 0 and vice versa. The circuit symbol and logic combinations for an NOT gate are as:

8 The NAND gate The NAND gate operates as an AND gate followed by a NOT gate. It acts in the manner of the logical operation "and" followed by negation. The output is "0" if both inputs are "1." Otherwise, the output is "1. The circuit symbol and logic combinations for a NAND gate are as:

9 The NOR gate The NOR gate is a combination OR gate followed by an inverter. Its output is "1" if both inputs are "0." Otherwise, the output is "0. The circuit symbol and logic combinations for a NOR gate are as:

10 The XNOR gate The XNOR (exclusive-nor) gate is a combination XOR gate followed by an inverter. Its output is "1" if the inputs are the same, and "0" if the inputs are different. The circuit symbol and logic combinations for the XNOR gate are as:

11 Logic Circuits A logic circuit is a combination of a number of logic gates. Using combinations of logic gates, complex operations can be performed. In theory, there is no limit to the number of gates that can be arrayed together in a single device. But in practice, there is a limit to the number of gates that can be packed into a given physical space. Arrays of logic gates are found in digital Integrated Circuits (ICs). As IC technology advances, the required physical volume for each individual logic gate decreases and digital devices of the same or

12 Examples 1. Make a truth table for the logic circuit shown below. Z P Q Y A B C X

13 2. Using the logic circuit below find the state of the output X.

14 Assignment 1. Using the logic circuit below, write the truth table. 2. Using the logic circuit below, write the truth table. 3. Using the logic circuit below, write the truth table.

15 4. Draw and name a logic gate that can produce the truth table below.

16 The SEVEN-SEGMENT DECODER A seven segment decoder is a digital circuit designed to drive a very common type of digital display device (Seven-segment display). A Seven-segment display is a set of LED (or LCD) segments that render numerals 0 through 9 at the command of a four-bit code. Seven-segment displays are a very common numerical interface for digital electronic equipment.

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18 ADDER (SUMMER) An adder or summer is a digital circuit that performs addition of numbers. In many computers and other kinds of processors, adders are used not only in the arithmetic logic units, but also in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators, and similar operations. The two basic types of adders are Half Adder and Full Adder.

19 HALF ADDER The half adder adds two single binary digits A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overflow into the next digit of a multi-digit addition. The addition of single bits can be done as shown: 0+0 = = = = 10 These are the least possible single-bit combinations. But the result for 1+1 is 10.

20 From the equation it is clear that this 1-bit adder can be easily implemented with the help of EXOR Gate for the output SUM and an AND Gate for the CARRY.

21 The implementation is as shown below.

22 FULL ADDER A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A, B, and C in ; A and B are the operands, and C in is a bit carried in from the previous less significant stage. The main difference between a half-adder and a full-adder is that the full-adder has three inputs, where as the half adder has two inputs. The first two inputs are A and B and the third input is an input carry designated as CIN.

23 The output carry is designated as COUT and the normal output is designated as S. The truth-table and circuit diagram are shown: