Page 259 - ARM 64 Bit Assembly Language

248 Chapter 8

fractional part of the number, and the radix point is nine bits to the right of the sign bit. The
layout for this number is shown graphically as:

where i is an integer bit and f is a fractional bit. Very small numbers with no integer part may
haveanegative i. For example, S(−7,16) specifies a signed number with no integer part, six
leading sign bits which are not actually stored, a sign bit that is stored and 15 bits of fraction.
The layout for this number is shown graphically as:

Note that the “hidden” bits in a signed number are assumed to be copies of the sign bit, while
the “hidden” bits in an unsigned number are assumed to be zero.

The following figure shows an unsigned fixed point number with seven bits in the integer part
and nine bits in the fractional part. It is a U(7,9) number. Note that the total number of bits is
7 + 9 = 16

The value of this number in base 10 can be computed by summing the values of each non-
zero bit as follows:
2 13−9 + 2 11−9 + 2 10−9 + 2 9−9 + 2 5−9 + 2 3−9 + 2 1−9 + 2 0−9