Motorola DSP56000, 24-Bit Digital Signal Processor manual Convergent Rounding

DATA REPRESENTATION AND ROUNDING

CASE I: IF A0 < $800000 (1/2), THEN ROUND DOWN (ADD NOTHING)

BEFORE ROUNDING

				0
	A2		A1			A0
XX . . XX		XXX . . . XXX0100			011XXX . . . . XXX
55	48 47		24 23			0

AFTER ROUNDING
		A2		A1		A0*
	XX	. . XX	XXX . . .	XXX0100	000 . . . .	. . . . 000
55	48 47		24 23		0

CASE II: IF A0 > $800000 (1/2), THEN ROUND UP (ADD 1 TO A1)

BEFORE ROUNDING

				1
	A2		A1			A0
XX . . XX		XXX . . . XXX0100			1110XX . . . . XXX
55	48 47		24 23			0

AFTER ROUNDING
		A2		A1		A0*
	XX	. . XX	XXX . . .	XXX0101	000 . . . .	. . . . 000
55	48 47		24 23		0

CASE III: IF A0 = $800000 (1/2), AND THE LSB OF A1 = 0,THEN ROUND DOWN (ADD NOTHING)

BEFORE ROUNDING

				0
	A2		A1			A0
XX . . XX		XXX . . . XXX0100			10000 . . . . . . 000
55	48 47		24 23			0

AFTER ROUNDING
		A2		A1		A0*
	XX	. . XX	XXX . . .	XXX0100	000 . . .	. . . . . 000
55	48 47		24 23		0

CASE IV: IF A0 = $800000 (1/2), AND THE LSB = 1, THEN ROUND UP (ADD 1 TO A1)

BEFORE ROUNDING

				1
	A2		A1			A0
XX . . XX		XXX . . . XXX0101			10000 . . . . . . 000
55	48 47		24 23			0

AFTER ROUNDING
	A2		A1		A0*
XX	. . XX	XXX . . .	XXX0110	000 . . . .	. . . . 000
55	48 47		24 23		0

*A0 is always clear; performed during RND, MPYR, MACR

Figure 3-10 Convergent Rounding

MOTOROLA DATA ARITHMETIC LOGIC UNIT 3 - 15