
48 CHAPTER 2 / NUMBER SYSTEMS, BINARY ARITHMETIC, AND CODES
to the BCD magnitude according to Eq. (2.11). Thus,
−0101 1001.0010 0100)
BCD
= (1 01011001.0010 0100)
BCD,2SM
.
2.6.3 Diminished Radix Complement Representation
The diminished radix complement N
(r−1)C
of a number N
r
having n digits is obtained by
N
(r−1)C
= r
n
− N
r
− 1, (2.15)
where, according to Eq. (2.12), N
(r−1)C
+ 1 = N
rC
. Therefore, it follows that
N
(r−1)C
=
¯
N
r
.
This means the diminished radix complement of a number is the digits complement of
that number as expressed by Algorithm 2.7. The range of representable n digit numbers in
diminished radix complement is −(r
n−1
− 1) through +(r
n−1
− 1) for radix ...