Answer to Question #151620 in Assembler for Raziya

Question

In 8087 math co-processors, what is the bias for a double precision floating point
representation? Demonstrate the conversion of a 64 bit floating point number into
corresponding decimal value.What is a descriptor in 80286 microprocessors? Write how the size of a memory
segment is determined during real mode memory addressing and during protected mode
memory addressing.

Answer 1

In double precision floating point the bias is 1023.

The general representation formula is:

(-1)^s * (1+mantissa) * 2^(Exponent – 1023)

 The value of decimal number is computed as:

The sign is stored in bit 63. The exponent can be computed from bits 62-52 by subtracting 1023. The mantissa is stored in bits 0-51.

An invisible leading bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 51 has a value of 1/2, bit 50 has value 1/4 etc. As a result, the mantissa has a value between 1.0 and 2

Sign

bit    Exponent                        Mantissa

 0     100 0000 0011     1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

(-1)^0   2^(1027--1023)                         1 + 1/2 + 1/4

1 * 16 * 1.75 =28

The 80286 and above operate in either the real or protected mode.

Real Address Mode

The contents of segment registers are used as segment base addresses. The other registers (size 16bits), depending upon the addressing mode, contain the offset addresses. As in 8086, the physical memory is organized in terms of segments of 64Kbyte maximum size.

RAM can be divided into logical blocks of 64 KB, called segments, with each segment starting at a multiple of 16 bytes. Thus, the first segment has a start address of 0, the second is at 16 (or 10 in hex), and so on  

 Protected Mode Memory Addressing

In protected mode, you can specify 64K and smaller segments than 64K.

80286 uses the 16-bit content of a segment register as a selector to address a descriptor stored in the physical memory. The descriptor is a block of contiguous memory locations containing information of a segment, like segment base address, segment limit, segment type, privilege level, segment availability in physical memory, descriptor type and segment use another task.

The descriptor for the i80286 processor is 8 bytes long. It consists of the following fields:

• the base address field, 24 bits long, contains the physical address of the segment described by this descriptor;

• the limit field contains the segment size in bytes, minus one;

• the access field describes the type of segment (code segment, data segment, etc.);

• the reserved 16-bit field for the i80286 processor must contain zeros, this field is used by the i80386 and i80486 processors