
Assume that 453 scientists have been invited to attend a conference. If every scientist is to be assigned
a unique bit pattern, what is the minimum number of bits required to do this?

How many more scientists can be invited to the conference, without requiring additional bits for each
person's unique id?
Problem 2 (8 points)
Using 7 bits to represent each number, write the representations of 25, 25 and 0 in signed magnitude,
1's complement and 2's complement notations.
Number  SignMagnitude  1's Complement  2's Complement 
25    
25    
0    
Problem 3 (4 points)
The following binary numbers are 5bit 2's complement binary numbers. Which of the
following operations generate overflow? Justify your answers by translating the operands
and results into decimal.

00111 + 00110

10111  11110

11000  00011

10110 + 10011
Problem 4 (2 points)
Compute the followings:

(10100 OR 01101) AND (NOT(10101))

(10101 OR 00100) AND (NOT(00101) OR 01010)
Problem 5 (4 points)
Convert the following decimal numbers into 6bit 2's complement binary numbers. Explain any
problem that you encounter for these conversions.

23

33

32

32
Problem 6 (2 points)
Perform the specified arithmentic operation for the following 2's complement binary numbers:

11001 + 1011

00111  010
Note:
 All numbers beginning with 1 are negative.
 Don't forget to signextend when required.
Problem 7 (4 points)
Write the decimal equivalents for the following IEEE floating point numbers.

1 01111110 01000000000000000000000

0 10000001 10100000000000000000000
Problem 8 (2 points)
Write the IEEE floating point representation of the decimal number 2.50.