CPU16
REFERENCE MANUAL
DIGITAL SIGNAL PROCESSING
MOTOROLA
11-3
The MAC accumulator uses 36-bit signed mixed numbers. The accumulator contains
36 bits. Bit 35 is the sign bit. Bits [34:31] are extension bits. Bits [30:0] are a 31-bit
fixed-point fraction. There is an implied radix point between bits 31 and 30. There are
31 bits of magnitude, but use of the sign and extension bits allows representation of
numbers in the range –16 ($800000000) to 15.999999999 ($7FFFFFFFF).
Figure 11-2
shows fractional data types and weighting of bits. Notice that signed frac-
tions and signed mixed numbers can be interpreted as different arithmetic values
when the same bits in the numbers are set.
Figure 11-2 MAC Data Types
11.5 MAC Accumulator Overflow
It is possible to accumulate to the point of overflow during successive and iterative
multiply and accumulate operations. Overflow becomes important when the 36-bit
number in AM is transferred to accumulator E by a TMER or TMET instruction. The
16-bit fraction in E does not have as great a range of values as the 36-bit number in
AM. Two types of overflow detection are used.
15
0
2
–
15
2
–1
2
–2
2
–3
2
–4
2
–5
2
–6
2
–7
2
–8
2
–9
2
–
10
2
–
11
2
–
12
2
–
13
2
–
14
±
(Radix Point) 16-BIT SIGNED FRACTION
31
16
2
–
15
2
–1
2
–2
2
–3
2
–4
2
–5
2
–6
2
–7
2
–8
2
–9
2
–
10
2
–
11
2
–
12
2
–
13
2
–
14
±
(Radix Point) MSW 32-BIT SIGNED FRACTION 1
15
2
–
16
0
2
–
31
0
2
–
17
2
–
18
2
–
19
2
–
20
LSW 32-BIT SIGNED FRACTION 1
2
–
21
2
–
22
2
–
23
2
–
24
2
–
25
2
–
26
2
–
27
2
–
28
2
–
29
2
–
30
35
32
2
1
31
2
0
16
2
–
15
2
3
2
2
2
–1
2
–2
2
–3
2
–4
2
–5
2
–6
2
–7
2
–8
2
–9
2
–
10
2
–
11
2
–
12
2
–
13
2
–
14
±
(Radix Point) MSW 32-BIT SIGNED FRACTION
15
2
–
16
0
2
–
31
2
–
17
2
–
18
2
–
19
2
–
20
2
–
21
LSW 32-BIT SIGNED FRACTION
2
–
22
2
–
23
2
–
24
2
–
25
2
–
26
2
–
27
2
–
28
2
–
29
2
–
30
F
Freescale Semiconductor, Inc.
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Go to: www.freescale.com
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.