DATA REPRESENTATION AND ROUNDING
3 - 14 DATA ARITHMETIC LOGIC UNIT
MOTOROLA
and rounds down any value below one-half. The question arises as to which way one-
half should be rounded. If it is always rounded one way, the results will eventually be
biased in that direction. Convergent rounding solves the problem by rounding down if the
number is odd (LSB=0) and rounding up if the number is even (LSB=1). Figure 3-10
shows the four cases for rounding a number in the A1 (or B1) register. If scaling is set in
the status register, the resulting number will be rounded as it is put on the data bus. How-
ever, the contents of the register are not scaled.
S S
.
.
.
SIGNED MULTIPLIER
SS MSP LSP •
2N — 1 PRODUCT
SIGN EXTENSION
2N BITS
S S
.
.
.
SIGNED MULTIPLIER
0
S•MSP LSP
2N — 1 PRODUCT
ZERO FILL
2N BITS
INTEGER FRACTIONAL
SIGNED MULTIPLICATION N x N - 2N – 1 BITS
Figure 3-9 Integer/Fractional Multiplication Comparison