Parhami
Chapter 1, Numbers and Arithmetic, Sections 1.11.6.
Chapter 2, Representing Signed Numbers, Sections 2.12.6.
Recommended reading (material covered during the next class)
Parhami
Chapter 17, Floatingpoint Representations.
Wikipedia
a. Determine how many digits are necessary to represent all possible values of the
A. sum of 64
integers in the range from 00_{16} to FF_{16 }each
B. product of 100 integers
in the range from 0 to 99_{ }each
using
 radix2 conventional system
 radix10 conventional system
 radix16 conventional system
b. Represent the following decimal numbers in hexadecimal representation.
864.6328125, 1567.19140625
c. Convert the following octal (radix8) numbers to hexadecimal (radix16) notation:
567251.436342, 347667.6242341
d. Represent 109.7109375 and 71.2890625
using the following binary signed number
representations with k = 8 and l = 8
 signed magnitude
 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. (Hint:
Apply formulas from Lecture 1, slide 70, "Extending the
number of bits of a signed number"). Convert
the obtained numbers to the decimal representation and show
that they have the same value as numbers you started with in
point e.
Problem 3 (bonus)
Prove
a formula for an extension of a signed number in the biased
representation with a kbit integer part and an lbit 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 1, slide 70,
"Extending the number of bits of a signed number").
Problem 4 (bonus)
Find
the contents of LUT F and LUT G in the implementation of a
5to3 parallel counter using a single CLB slice of a Virtex
FPGA (see slides from Lecture 4).