Chapter 1, Numbers and Arithmetic, Sections 1.1-1.6.
Chapter 2, Representing Signed Numbers, Sections 2.1-2.6.
Chapter 17, Floating-point Representations.
a. Determine how many digits are necessary to represent all possible values of the
A. sum of 1024 integers
the range from 0016
B. product of 1000 integers in the range from 0 to 99 each
- radix-2 conventional system
- radix-10 conventional system.
b. Represent the following decimal numbers in hexadecimal representation.
c. Convert the following octal (radix-8) numbers to hexadecimal (radix-16) notation:
Represent -123.7109375 and
using the following binary signed number representations with k = 8 and l = 8
- one's complement
- two's complement
- biased with the base B=128.
e. Extend all numbers from point d., expressed in the respective signed number representations with k = 8 and l = 8, to the numbers with the same value and the sizes of the integer and fractional part equal respectively to k' = 16 and l' = 16 (see Lecture 4, slide 71, "Extending the number of bits of a signed number").
Problem 2 (3 bonus points)
Prove a formula for an extension of a signed number in the biased representation with a k-bit integer part and an l-bit fractional part to a number with a k'-bit integer part and an l'-bit fractional part, with k' > k and l' > l (see Lecture 4, slide 71, "Extending the number of bits of a signed number").
bits of the ANSI/IEEE standard single-precision
representation of the following numbers (Hint:
use default rounding scheme if necessary):
Problem 4 (2 bonus points)
Consider the IEEE 32-bit standard floating-point format.
Can floating-point numbers be compared by treating their representations as signed integers in the signed magnitude representation, even when denormals and +/- infinity are considered?
If your answer
is yes, please prove this property of the floating point representation.
If your answer is no, please provide a counterexample.