1. Consider 4-bit BINARY numbers, because of “roll-over” the number line wraps around.
Perform the following additions:
e) for unsigned numbers: 0100
2
(4
10
) 1001
2
(9
10
)
+ 0110
2
(6
10
)+ 1010
2
(10
10
)
f) for signed numbers: 0100
2
(4
10
) 0100
2
(4
10
)1100
2
(-4
10
)
(two’s compliment) + 0110
2
(6
10
)+ 1010
2
(-6
10
) + 1010
2
(-6
10
)
2. For 4-bit unsigned numbers, when do we have overflow and get the wrong result during
addition? (Hint: think about the carry bits into and/or out of the most-significant bit)
3. a) For 4-bit signed numbers, complete the following table about signed overflow:
-
-
+
-
These two rows cannot cause
signed overflow in addition
-
+
++
Operand 2Operand 1
Wrong Sign
of Result
(indicates overflow)
Expected Sign
of Result
Sign of Operands for addition
b) For 4-bit signed numbers, when do we have overflow and get the wrong result during
addition? (Hint: think about the carry bits into and/or out of the most-significant bit)
4. How would you subtract two signed, 2’s-complement numbers? Try the following:
0110
2
(6
10
) 0011
2
(+3
10
)1111
2
(-1
10
)
- 0111
2
(7
10
)- 1111
2
(-1
10
) - 0011
2
(+3
10
)
Comp. Org. (CS 1410) Lecture 3 Name:________________
Lecture 3 Page 1
0000 0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
a) List unsigned decimal values on the outside
b) List signed (two's complement) decimal
values on the inside
c) Mark the point of unsigned overflow
d) Mark the point of signed overflow
Docsity.com
