ITC 544 Computer Organisation And Architecture

A Computer uses IEEE-754 single precision format to represent floating points. What value (in decimal) the computer represents if the floating point is represented using the following binary digits:

 

b) Using a "word" of 5 bits, list all of the possible signed binary numbers and their decimal equivalents that are represent able in: 
i. Signed magnitude
ii. One's complement
iii. Two's complement

 

a) Write a Boolean function and construct a logic diagram of a circuit which use of basic logic gates to activate CSU main entrance door during 9:00 am to 12:00 pm and after lunch time during 1:00 pm - 4:00 pm. You need to use 24 hour clock timing when designing this circuit.

 

Please insert the Boolean expression, minimisation, and the diagram

b) Using basic Boolean algebra identities for Boolean variables A, B and C, prove that X’Y + XYZ’ + Y’ + XZ (Y+Y’) = 1. Please show all steps and mention the identities used.

The computer will represent 8.125 * 10^-1 if the floating point is represented using 0 01111110 10100000000000000000000

0 1010 (5-bit word)

Signed magnitude- +10 because the most significant bit is 0 and the rest 4 bits are magnitude

One’s complement- 10101

Two’s complement- 10110

The below table is representing the hours of the clock in 5-bit binary form.

Magnitude	Binary					Clock pulse (p)
1	A	B	C	D	E	High (+1)
	00001
2	00010
3	00011
4	00100
5	00101
6	00110
7	00111
8	01000
9	01001
10	01010
11	01011
12	01100
13	01101					Low (0)
14	01110
15	01111
16	10000
17	10001
18	10010
19	10011
20	10100
21	10101
22	10110
23	10111
24	11000

The logic diagram is:

A'BC'D'EP+A'BC'DE'P+A'BC'DEP+A'BCD'E'P=Q (For clock= +1)

A'BCD'EP’+A'BCDE'P’+A'BCDEP’+AB'C'D'E'=R (For clock=0)

 

X’Y+XYZ’+Y’+XZ (Y+Y’)

= X’Y+XYZ’+Y’+XZY+XZY’

= X’Y+XY (Z+Z’) +Y’+XZY’

=X’Y+XY+Y’+XZY’

=Y+Y’+XZY’

=1+XZY’

=1 (PROVED)