(1) 5 points What decimal value is represented by the IEEE single precision floating point value 0xc2290000 ?
0xc2290000 can be represented in floating point notation as
S E F
1 10000100 01010010000000000000000
exponent e = E-127 = 5
Decimal value D = - 1.01010010..0 * (2**5)
= - 101010.010..0
= - 42.25
(2) 6 points Perform the following operations. Assume that the operands and the results are integers represented as 8-bit 2's complement integers. Indicate which ( if any ) of the operations cause overflow.
10101010 00001111 10001001
+ 11011000 + 10001111 - 01100000 (add 2's complement
of 01100000)
---------- ----------- -----------
1<- 10000010 0<-10011110 1<-00101001
No overflow No overflow Overflow
Overflow occurs if the MSB of both added integers are the same
and that of the result is different.
(3) 6 points Perform the following operations. Assume that the operands and the results are integers represented as 8-bit sign magnitude integers. Indicate which (if any) of the operations cause overflow.
1 0101010 0 0001111 1 0001001
+ 1 1011000 + 1 0001111 - 0 1100000 (X-Y = X+(-Y)
Hence make sign
bit 1)
---------- ----------- -----------
0000010 1101001
| |
1 0
(Carry) (Carry)
Overflow No overflow No overflow
Overflow occurs only if there is a carry out of the magnitude
bits. We need to calculate sum only if both signs are the same.
(4) 5 points Perform the following multiplication. Assume that both operands are 5-bit 2's complement integers and the result is a 10-bit 2's complement integer.
11010 ---> 11111 11010 ( -6 ) // Sign extension
* 11000 ---> 11111 11000 ( -8 )
--------- ------------
00000 00000
00000 0000
00000 000
11110 10
11101 0
11010
1010
010
10
0
-----------
00001 10000 ( 48 )
-----------
(5) 6 points What are the values of the variables aa,bb and cc after the following SAL code completes? Give the results in hexadecimal.
.data______________________________________________________________________________aa: .word 0x000000aa bb: .word 0xe00000ff cc: .word 0xcc112233
.text
nand aa,aa,bb xor bb,bb,aa sll cc,cc,3 done
Solution
aa = 0xffffff55 bb = 0x1fffffaa cc = 0x60891198