The NOR function is a dual of the NAND function. For this reason, the implementation procedures and rules for NOR-NOR logic are the duals of the corresponding procedures and rules developed for NAND-NAND logic.
NOR-NOR Implementation AU:
May-11
• The NOR function is a dual of the NAND
function. For this reason, the implementation procedures and rules for NOR-NOR
logic are the duals of the corresponding procedures and rules developed for
NAND-NAND logic.
• The implementation of a Boolean function
with NOR-NOR logic requires that the function be simplified in the product of
the sum form.
• In product of sum form, we implement
all sum terms using Or gates.This constitutes the first level.
• In the second level all sum terms are
logically ANDed using AND gate. The relationship between OR-AND logic and
NOR-NOR is explained using following example.
• Consider the Boolean function : Y =(A +
B + C) (D + E) F
• This Boolean function can be
implemented using OR-AND logic, as shown in the Fig. 1.9.1 (a).
• Fig. 1.9.1 (b) shows the OR gates are
replaced by NOR gates and the AND gate is replaced by a bubbled AND gate. The
implementation shown in Fig. 2.16.1 (b) is equivalent to implementation shown
in Fig. 2.16.1 (a), because two bubbled on the same line represent double
inversion (complementation) which is equivalent to having no bubble on the
line.
• In case of single variable, F, the
complemented variable again complemented by bubble to produce the normal value
of F.
• In Fig. 1.9.1 (c), the output NOR gate
is redrawn with the conventional symbol. The NOR gate with same inputs gives
complemented result, therefore, is replaced by NOR gate with F input
to its both inputs. Thus all the three implementations of Boolean function are
equivalent.
Rules for obtaining the NOR-NOR logic
diagram
1. Simplify the given Boolean function
and express it in product of sum form (POS form).
2. Draw a NOR gate for each sum term of
the function that has two or more literals. The inputs to each NOR gate are the
literals of the term. This constitute a group of first level gates.
3. If Boolean function includes any
single literal or literals, draw NOR gate for each single literal and connect
corresponding literal as an input to the NOR gate.
4. Draw a single NOR gate in the second
level, with inputs coming from outputs of first level gates.
Illustrative Examples
Example 1.9.1
Implement the following Boolean function with NOR-NOR logic
Y=AC+BC+ A B+ D.
Solution: Step 1:
Express Boolean function in POS form.
Using duality theorem we get,
Example 1.9.2
Implement the following Boolean function with NOR-NOR logic. F = (A, B, C) = II
M (0, 2, 4, 5, 6)
Note It is possible
to directly go to step 3 skipping step 2. Here, step 2 is included for clear
understanding.
Example 1.9.3
Design a combinational circuit that comprises only of NOR gates for the
following expression giving the input output relation.
Y = ABC' + AC + B'C. AU May-11, Marks
10
Solution :
Digital Principles and Computer Organization: Unit I: Combinational Logic : Tag: : Combinational Logic - Digital Principles and Computer Organization - NOR-NOR Implementation
Digital Principles and Computer Organization
CS3351 3rd Semester CSE Dept | 2021 Regulation | 3rd Semester CSE Dept 2021 Regulation