Parhami

Chapter 1, Numbers and Arithmetic, Sections 1.1-1.6.

Chapter 2, Representing Signed Numbers, Sections 2.1-2.6.

Recommended reading (regarding current lecture)

Deschamps, Bioul, Sutter

Chapter 3.1.1, Weighted Systems.

Chapter 3.2, Integers, Sections 3.2.1-3.2.3.

## Recommended reading (material covered during the next class)

Parhami

Chapter 17, Floating-point Representations.

Deschamps, Bioul, Sutter

Chapter 3.3, Real Numbers.

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

- radix-2 conventional system

- radix-10 conventional system

- radix-16 conventional system

b. Represent the following decimal numbers in hexadecimal representation.

864.6328125, 1567.19140625

c. Convert the following numbers from radix 10 to radix 5

367.425, 555.555

d. Convert the following octal (radix-8) numbers to hexadecimal (radix-16) notation:

567251.436342, 347667.6242341

e.
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.

f. Extend all numbers from point e.,
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 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 1,
slide 70, "Extending the number of bits of a signed number").