Exclusive-OR and Exclusive-NOR Gates Chapter 6 Exclusive-OR and Exclusive-NOR Gates 1

Objectives You should be able to: Describe the operation and use of exclusive-OR and exclusive-NOR gates. Construct truth tables and draw timing diagrams for exclusive-OR and exclusive-NOR gates. Simplify combinational logic circuits containing exclusive-OR and exclusive-NOR gates. 2

Objectives (Continued) Design odd- and even-parity generator and checker systems. Explain the operation of a binary comparator and a controlled inverter. Implement circuits in FPGA ICs using VHDL. 2

The Exclusive-OR Gate The output is HIGH if either one or the other inputs are HIGH., but not both. 4

The Exclusive-OR Gate Logic circuits for the exclusive-OR function. 5

The Exclusive-OR Gate Logic Symbol and Boolean equation 6

The Exclusive-NOR Gate The complement of the exclusive-OR. Often called an equality gate: The output is HIGH when the inputs are equal. 7

The Exclusive-NOR Gate Ex-NOR Logic Circuit 8

The Exclusive-NOR Gate EX-NOR Logic Symbol and Boolean equation 9

Parity Generator / Checker Electrical noise in the transmission of binary information can cause errors. Parity can detect these types of errors. Parity systems Odd parity Even parity Adds a bit to the binary information 10

Parity Generator / Checker Odd parity generator/checker 11

Parity Generator / Checker Four-bit even- and odd-parity generators 12

Parity Generator / Checker Eight-bit even-parity generator 13

Parity Generator / Checker Five bit even-parity checker 14

Parity Generator / Checker Integrated-Circuit Parity Generator/Checker 74280 TTL IC logic symbol and Function Table 15

Parity-Error Detection System 17

Parallel Binary Counter

Controlled Inverter 19

Discussion Point Describe the operation of an exclusive OR and an exclusive NOR gate. Design an exclusive OR gate from NOR gates. 20

Discussion Point Does the circuit below function as an even or odd parity generator? 21

FPGA Design Applications with VHDL New concepts included in examples 6-8 though 6-10: 7400-series macro-functions Grouping nodes to a common bus Changing a group’s radix Creating a VHDL Process Statement and For Loop. 22

Example 6-8 The Quartus II software provides the original 74280b in the bdf file. Note that the inputs are grouped as a bus.

Example 6-8 The radix can be changed in the simulation report of the vwf file.

Example 6-9 Each node line coming off a bus must be labeled correctly for the compiler.

Example 6-9 The hex counter values can be forced to inequality by highlighting the number choosing Value > Arbitrary Inserting a new value

Example 6-10 Note that both the data inputs and the controlled output are grouped as a bus.

Example 6-10 When c is low the output is uncomplemented. When c is high the output is complemented.

Example 6-10 An example of a sequential process loop.

Summary The exclusive-OR gate provides a HIGH output if one input or the other input, but not both, is HIGH. The exclusive-NOR gate outputs a HIGH if both inputs are HIGH or if both inputs are LOW. 24

Summary A parity bit is commonly used for error detection during the transmission of digital signals. Exclusive-OR and exclusive-NOR gates are used in applications such as parity checking, binary comparison and controlled complementing circuits. FPGAs can be used to implement circuits containing the exclusive gates. 25