The second example is a very large number7665543322211111_{8}; refer to figure 5-15, frame B.After the number has been put in exponent form, it, too,will require two 32-bit words.FLOATING-POINT PRECISION.— Floating-point formats include the use of single- anddouble-precision (refer to figure 5-16, frames A and B).The names single- and double-precision imply theirusefulness: precision.Notice the double-precisionfloating-point format, two 32-bit words where thecharacteristic is small compared to the mantissa inwhich precision accuracy is required.FLOATING-POINT ROUND.— Floating-pointoperations also include rounding instructions, whichare used for rounding the mantissa’s results; roundingup when the mantissa is equal to or greater than one-halfof one and rounding down when it less than one-half ofone. Rounding can also be applied to double-lengthresults of mantissas.If the sign bit is destroyed(overflowed into) during mantissa rounding or division,the computer will make corrections to the mantissa orquotient.FLOATING-POINT INTERRUPTS.— Float-ing-point interrupts can be generated when certainimproper conditions are detected. The interruptsinform the program of these conditions and permiteither notation or corrective procedures. Someconditions include:l Underflow (negative excess) oroverflow(posi-tive excess)—When a floating-point char-acter exceeds an absolute value of 2^{N}-1 whereN is the msb.l Divisor—Equals zero in a divide instructionThe control section will be notified and an interruptwill be generated.Figure 5-16.—Floating-point numbers: A. Single precision; B. Double-precision.5-22