Freescale Semiconductor SC140 specifications Data Formats, Signed Fractional

DALU

16-bit word operand

D0.h—D15.h,

16-bit memory

40-bit registers	–28
D0—D15

–20 2–15

20 2–15 2–16 2–31

16-bit word operand

D0.l—D15.l,

16-bit memory

40-bit registers

D0—D15

Signed Fractional Two’s Complement Representations

			–215	214	20	.
–239	231	216			20
						.
			215

Signed Integer Two’s Complement Representations

Figure 2-3. DALU Data Representations

2.2.2.2 Data Formats

Three types of two’s complement data formats are supported by the SC140 core:

•Signed fractional (SF)

•Signed integer (SI)

•Unsigned integer (UI)

The ranges for each of these formats, described below, apply to all data stored in memory as well as data stored in the data registers. The extension associated with each register allows word growth so that the most positive fractional number that can be represented in a register is almost 256.0 with the most negative fractional number being exactly -256.0. When the register extension is in use, the data contained in the register cannot be stored exactly in memory or in other registers in a single move. In these cases, the storage error can be minimized by limiting the data to the most positive or most negative number consistent with the size of the destination, the sign of the register and the MSB of the extension.

2.2.2.2.1 Signed Fractional

In this format, without extension bits 39-32, the N-bit operand is represented using the 1.[N-1] bit format (1 sign bit, N-1 fractional bits). Signed fractional numbers lie in the following range:

-1.0 ≤ SF ≤+1.0 - 2-[N-1]

For words and long-word signed fractions, the most negative number that can be represented is exactly –1.0, of which the internal representation is $8000 and $8000 0000, respectively. The most positive word is $7FFF or 1.0–2-15, and the most positive long word is $7FFF FFFF or 1.0–2-31.

If the extension bits are in use, the most positive number is 256 – 2–31represented by $7F FFFF FFFF, and the most negative number is –256, represented by $80 0000 0000.

2-18 SC140 DSP Core Reference Manual