Scribd
Upload
136 views17 pages

NAND-NOR Implementation

The document discusses implementing Boolean functions with NAND and NOR gates. It describes how to express functions in sum-of-products form and then draw logic diagrams with gates for each product term. Multilevel circuits with more than two levels are also discussed. Exclusive OR functions are odd functions where an odd number of variables must be 1.

Uploaded by

A N Jayanthi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
136 views17 pages

NAND-NOR Implementation

The document discusses implementing Boolean functions with NAND and NOR gates. It describes how to express functions in sum-of-products form and then draw logic diagrams with gates for each product term. Multilevel circuits with more than two levels are also discussed. Exclusive OR functions are odd functions where an odd number of variables must be 1.

Uploaded by

A N Jayanthi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 17

NAND/NOR Implementation

• A convenient way to implement a Boolean


function with NAND / NOR gates is to obtain
the simplified Boolean function in terms of
Boolean operators and then convert the
function to NAND/NOR logic
NAND Gates
Logic operations with NAND gates
NAND Gates

The implementation of Boolean functions with NAND gates requires that the
functions be in sum-of-products form.
Two level Implementation using only NAND
gates for F= AB + CD
Procedure
The procedure for obtaining the logic diagram from a Boolean function is as follows:
1. Simplify the function and express it in sum-of-products form.
2. Draw a NAND gate for each product term of the expression that has at least two
literals. The inputs to each NAND gate are the literals of the term. This procedure
produces a group of first-level gates.
3. Draw a single gate using the AND-invert or the invert-OR graphic symbol in the second
level, with inputs coming from outputs of first-level gates.
4. A term with a single literal requires an inverter in the first level. However, if the single
literal is complemented, it can be connected directly to an input of the second level
NAND gate.
Multilevel NAND Circuits
There are occasions, however, when the design of digital
systems results in gating structures with three or more levels.
The most common procedure in the design of multilevel
circuits is to express the Boolean function in terms of AND, OR,
and complement operations.
The function can then be implemented with AND and OR gates.
After that, if necessary, it can be converted into an all-NAND
circuit.
Multilevel NAND Circuits
NOR gates

Logic operations with NOR gates


Two graphic symbols for the NOR gate
F = (A + B)(C + D)E

Implementing F = (A + B)(C + D)E

Implementing F = (AB’ + A’B)(C + D’) with NOR gates


Exclusive-OR implementations
Exclusive-OR implementations
• The Boolean expression clearly indicates that the
three-variable exclusive-OR function is equal to 1
if only one variable is equal to 1 or if all three
variables are equal to 1. Contrary to the two-
variable case, in which only one variable must be
equal to 1, in the case of three or more variables
the requirement is that an odd number of
variables be equal to 1. As a consequence, the
multiple-variable exclusive-OR operation is
defined as an odd function.
Exclusive-OR implementations

Map for a three-variable exclusive-OR function

EXCLUSIVE – OR EXCLUSIVE NOR


3 variable Odd/Even Function
4 variable Odd/Even Function
THANK YOU

You might also like