Chapter 1, Numbers and Arithmetic, Sections 1.1-1.6.
Chapter 2, Representing Signed Numbers, Sections 2.1-2.6.
Recommended reading (material covered during the next class)
Chapter 17, Floating-point Representations.
a. Determine how many digits are necessary to represent all possible values of the
A. sum of 64
integers in the range from 0016 to FF16 each
B. product of 100 integers in the range from 0 to 99 each
- radix-2 conventional system
- radix-10 conventional system
- radix-16 conventional system
b. Represent the following decimal numbers in hexadecimal representation.
c. Convert the following octal (radix-8) numbers to hexadecimal (radix-16) notation:
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
Problem 3 (bonus)
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 1, slide 70,
"Extending the number of bits of a signed number").
Problem 4 (bonus)
the contents of LUT F and LUT G in the implementation of a
5-to-3 parallel counter using a single CLB slice of a Virtex
FPGA (see slides from Lecture 4).