Programming and Graphics

1.7 The hexadecimal system 23

representation in single precision using four-byte word lengths that accommo-
date eight hexadecimal digits. Assume that the hexadecimal representation of
a stored number is:

0x3F800000 (40)

The associated binary string is:

0 011 1111 1000 0000 0000 0000 0000 0000. (41)

In Section 1.6, we saw that this is the floating point representation of 1.0.

Problems

1.7.1.Compute the hexadecimal representation of 66.75.

1.7.2.Derive in hexadecimal form the single-precision, hidden-bit floating point
representation of the number (a) 0.125, and (b) -40.5.

1.7.3.A number in the octal system is denoted as

(okok− 1 ···o 0 .o− 1 ···o−l) 8 (42)

wherekandlare two integers, the octal charactersoitake eight values

0–7, and the period (.) is the octal point. The corresponding decimal

value is

ok× 8 k+ok− 1 × 8 k−^1 +···+o 0 × 80 +o− 1 × 8 −^1 +···+o−l× 8 −l.

(43)

(a) Write the octal representation of zero and first seventeen integers.

(b) To find the octal representation of a given binary string, we start from

the left or right or the binary point, divide the binary string into blocks

of two digits, and look up the octal digit corresponding to each block.

Apply this procedure to find the octal representation of (101111) 2.