Computer Arithmetic - Fundamentals of Computer Organization and Architecture - page 79

Figure 4.17 Double-precision representation

TABLE 4.2 Characteristics of the IEEE Single and Double
Floating-Point Formats

Characteristic Single-precision Double-precision

Length in bits 32 64

Fraction part in bits 23 52

Hidden bits 1 1

Exponent length in bits 8 11

Bias 127 1023

2 128 3 : 8 10 38 2 1024 9 : 0 10 307 Approximate range

2 126 10 38 2 1022 10 308

Smallest normalized number

A number of attributes characterizing the IEEE single- and double-precision
formats are summarized in Table 4.2.

4.4. SUMMARY

In this chapter, we have discussed a number of issues related to computer arithmetic.
Our discussion started with an introduction to number representation and radix con-
version techniques. We then discussed integer arithmetic and, in particular, we dis-
cussed the four main operations, that is, addition, subtraction, multiplication, and
division. In each case, we have shown basic architectures and organization. The
last topic discussed in the chapter has been floating-point representation and arith-
metic. We have also shown the basic architectures needed to perform basic float-
ing-point operations such as addition, subtraction, multiplication, and division.
We ended our discussion in the chapter with the IEEE floating-point number
representation.

EXERCISES

1. Represent the decimal values 26, 123 as signed, 10-bit numbers using each

2

of the following binary formats:
(a) Sign-and-magnitude;
(b) 2's complement.
2. Compute the decimal value of the binary number 1011 1101 0101 0110 if the
given number represents unsigned integer. Repeat if the number represents
2's complement. Repeat if the number represents sign-magnitude integer.