Interpreting 10s complement codes
Humans are trained to represent signed values using the sign-magnitude rperesentation:
Interpreting 10s complement codes
We have just learned a new representation for signed values:
Interpreting 10s complement codes
Question: how do we convert between these 2 representations ?
Note: the conversion must preserve the represented value !!
Converting a sign-magnitude code
into a
(3 digit) 10s complement code
Question: what's the (3 digit) 10s compl code for 34 and −34 ?
Consider the mapping that we discussed previously:
3 digit
10s compl code
(odometer code)
500 996 997 998 999 000 001 002 003 004 499
+---+...+---+---+---+---+---+---+---+---+...+---+
•••• ••• •• • ( ) • •• ••• ••••
-500 -4 -3 -2 -1 0 1 2 3 4 499
Signed value
|
We must
consider 2 cases:
(1) when the value is
positive (or ZERO)
and
(2) when the value is
negative
Converting a sign-magnitude code
into a
(3 digit) 10s complement code
How to
encode (= represent) a
positive value as
a (3 digit)
10s complement code:
3 digit
10s compl code
(odometer code)
500 996 997 998 999 000 001 002 003 004 499
+---+...+---+---+---+---+---+---+---+---+...+---+
•••• ••• •• • ( ) • •• ••• ••••
-500 -4 -3 -2 -1 0 1 2 3 4 499
Signed value
|
Converting
positive values (and ZERO):
Prepend the
sign-magnitude code with
leading ZEROs
until you have
3 digits
Example: the (3 digit) 10s compl code for 34 is: 034
Note: adjust the number of leading ZEROs to the length of the 10s complement code
Converting a sign-magnitude code
into a
(3 digit) 10s complement code
How to
encode (= represent) a
negative value as
a (3 digit)
10s complement code:
3 digit
10s compl code
(odometer code)
500 996 997 998 999 000 001 002 003 004 499
+---+...+---+---+---+---+---+---+---+---+...+---+
•••• ••• •• • ( ) • •• ••• ••••
-500 -4 -3 -2 -1 0 1 2 3 4 499
Signed value
|
Converting
negative values:
(3 digit) 10s complement code =
1000 −
abs(sign-mag code)
Example: the (3 digit) 10s compl code for −34 is: 1000 − 34 = 966
Finding the sign-magnitude code
for a
(3 digit) 10s complement code
Question: what's the signed values for the (3 digit) 10s compl codes 066 and 734 ?
Consider the mapping that we discussed previously:
3 digit
10s compl code
(odometer code)
500 996 997 998 999 000 001 002 003 004 499
+---+...+---+---+---+---+---+---+---+---+...+---+
•••• ••• •• • ( ) • •• ••• ••••
-500 -4 -3 -2 -1 0 1 2 3 4 499
Signed value
|
Notice that:
Codes that starts with a digit
0,1,2,3,4 represents
positive values (and ZERO)
Codes that starts with a digit
5,6,7,8,9 represents
negative values
Finding the sign-magnitude code
for a
(3 digit) 10s complement code
How to find the (positive) value of a (3 digit) 10s complement code that starts with 0,1,2,3 or 4:
Example: 066
3 digit 10s compl code (odometer code) 066=?? 500 996 997 998 999 000 001 002 003 004 499 +---+...+---+---+---+---+---+---+---+---+...+---+ •••• ••• •• • ( ) • •• ••• •••• -500 -4 -3 -2 -1 0 1 2 3 4 499 Signed value |
Decoding a
10s compl code that starts
with 0,1,2,3, or 4:
Read the
10s complement code
as a (positive) value -
possibly ignoring
the leading ZEROs.
Example: the signed value represented by 066 is: 66
Finding the sign-magnitude code
for a
(3 digit) 10s complement code
How to find the (negative) value of a (3 digit) 10s complement code that starts with 5,6,7,8, or 9:
Example: 734
3 digit 10s compl code (odometer code) 734=?? 500 996 997 998 999 000 001 002 003 004 499 +---+...+---+---+---+---+---+---+---+---+...+---+ •••• ••• •• • ( ) • •• ••• •••• -500 -4 -3 -2 -1 0 1 2 3 4 499 Signed value |
Decoding a
10s compl code that starts
with 5,6,7,8, or 9:
(Signed) value =
−
(1000 −
10s compl code)
Example: the value represented by 734 is: − (1000 − 734) = −266