1.

C

onvert the following base 2 numbers to base 10 and to base 16:

a.

0110 1010

b. 0000 1010 0110 1100

2.

C

onvert each of the following hexadecimal (base

16) numbers to base 2 and to base 10:

a.

0A54H

b 2C74H

3.

C

onvert the following base 10 numbers to base 2 and to base 16:

a.

253

b. 64,327

4.

C

onvert each of the following numbers to base 2 negative numbers in the twos complement format:

a.

253

10

(using

8

-

bit

s)

b. 0110 1010

2

(using

8

-

bit

s)

c.

(using 16

-

bit

s) 2C74H

5.

Floating point numbers are usually stored in computers using the IEEE

754 format.

Do some research on the IEEE 754 format and scientific notation,

and answer the

following qu

estions relate

d

to

the IEEE 754 format

:

a.

describe the single precision (binary 32) IEEE format.

b.

describe the double precision (binary 64)

IEEE format.

c.

one part of a number in the IEEE 754 format is called the

significand

. Its original proper

mathematical

na

me is

mantissa

. How is

this

value in scientific notation

different from a mantissa in a logarithm? Why does the IEEE suggest that this part of a floating point

number be

called a significand rather than a mantissa?

d.

Show what 2

3.145

* 2

2.861

equals as a power of 2

. In general, what do we do to two exponents when multiplying numbers that have the

same base?

e.

W

hat we do with the significands when

multiplying

two

numbers in scientific notation, such

a

s

:

(

3.47

*

10

2

)

* (

2.181

*

10

3

)

?

Note: Scientific notation is a

log

-

linear

numeric format, compared to a log only format

,

such as log

2

(200

) = 7.643

856

6.

Sh

ow the hexadecimal code for your

first

name

stored as

as a Unicode UTF 16 s

tring.