2.11. XOR Properties and Applications
K-map patterns
Checkerboard pattern: alternating cells and diagonal cells of 1s and 0s on a K-map is a sign of XOR
or XNOR.
XOR properties:
Commutative
A⊕B⊕C=C⊕B⊕A Associative
A⊕(B⊕C)=(C⊕B)⊕A Rubber band effect (The bar can be put anywhere and the result remains unchanged)
A⊕B=A⊕B=A⊕B=A⊕B XOR is 1 when there is an odd number of 1’s in the XOR operands
Note: This feature is used to do single bit error checking, which is adding an extra bit to the
data to ensure that the number of 1’s is odd. (This is known as odd parity). XNOR is 1 when there is an even number of 1’s in the XNOR operands
Note that this feature is used to do single bit error checking, which is adding an extra bit to
the data to ensure that the number of 1’s is even. (This is known as even parity). XNOR 4-bit Comparator DesignA 0
B 0
1 if A 0 = B 0A 1
B 1
A 2
B 2
A 3
B 3
A=B 1 if A 0 = B 0 and
A 1 = B 1 and A 2 = B 2
and A 3 = B 3.0 1
0 1
1 0
1 0
AB
C (^) 0 1
00
01
11
10
0 1
0 0
1 0
0 0
AB
C (^) 0 1
00
01
11
10
0 0
0 0
1 1
1 1
AB
C (^) 0 1
00
01
11
10
Checkerboard pattern
F = A⊕B⊕C
Diagonal Cells
F = A.(B⊕C)
Alternating Cells
F = A⊕B