Computer Sciene hw

1. Assume we are using the Simple Model for floating - point representation ( the representation uses a 14 - bit format, 5 bits for the exponent with a bias of 16 , a normalized mantissa of 8 bits, and a single sign bit for the number ) . Show how the computer would represent the numbers 12.125 and 0.675 using this floating - point format.

12.125 =

single sign bit ( 1 bit )	exponent with a bias of 16 ( 5 bits )	normalized mantissa ( 8 bits )

0.675 =

single sign bit ( 1 bit )	exponent with a bias of 16 ( 5 bits )	normalized mantissa ( 8 bits )

2. Verify De Morgan's Laws are valid by completing this truth table of one of his laws.

x	y	( x y )'	x ' + y '
1	1
1	0
0	1
0	0

3. Is the following distributive law valid or invalid? Prove your answer by completing these truth tables.

x XOR ( y + z ) = ( x XOR y ) + ( x XOR z )

x	y	z	x XOR ( y + z )
1	1	1
1	1	0
1	0	1
1	0	0
0	1	1
0	1	0
0	0	1
0	0	0

x	y	z	( x XOR y ) + ( x XOR z )
1	1	1
1	1	0
1	0	1
1	0	0
0	1	1
0	1	0
0	0	1
0	0	0

4. Attempt to minimize the following circuit defined by the following Boolean function:

C ( x , y , z ) = x y z + x ' y ' z + x ' y z

where x ' represents the complement of x

5 . If the HD of a PC is advertised as a 256 GB capacity, what is the actual amount of bytes on it ( assuming the original size was Base 2 ) ?