Computer Science 134
Homework 9
Due: 11 December 2009
Question 1. When a single parity bit is added to a binary message, all errors that alter an odd number of bits will
be detected, and all errors that modify an even number of bits will go undetected. Things get a bit trickier when 2
dimensional parity bits are used. Depending on the number of bits altered by an error we can either say:
(A) All errors containing this number of bits will be detected, or
(B) Some errors containing this number of bits will be detected and others will go undetected.
For each type of error described below, indicate which of these two options describes the way a 2 dimensional parity
scheme would handle such errors. In each case, if you answer (A), provide one example of an error that would be
detected by modifying the bits in the ”Detectable Error” table provided (and leave the ”Undetectable Error” table
unchanged. If you answer (B), provide one example of an error that would be detected in the ”Detectable Error” table
and another of an error that would go undetected in the ”Undetectable Error” table. In all cases, assume that the parity
bits are only being used to detect errors. That is, assume that if any row or column contains a odd number of 1’s that
the data will be treated as an error without making any attempt to correct the error.
3 Bit Detectable Error
.
3 Bit Undetectable Error
(a) 3 bit errors:
A
or B
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
.
4 Bit Detectable Error
.
4 Bit Undetectable Error
(b) 4 bit errors:
A
or B
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
.
5 Bit Detectable Error
.
5 Bit Undetectable Error
(c) 5 bit errors:
A
or B
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
.
6 Bit Detectable Error
.
6 Bit Undetectable Error
(d) 6 bit errors:
A
or B
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
C