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homework solutions of some assignments from jacob savir's ece 251 course
Typology: Exercises
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ECE251 Digital DESIGN
66 0 33 1 16 0 8 0 4 0 2 0 1 1 0
Therefore, the 2’s complement representations of +66 and –66 using 8-bits are:
,
1.()b Long division:
Therefore,.
1.()c Long division:
72 0 36 0 18 0 9 1 4 0 2 0 1 1 0
Therefore, the 2’s complement representations of +72 and –72 using 8-bits are:
,.
1.()d Long division:
55 1 27 1 13 1 6 0 3 1 1 1 0
Therefore,.
, ,
The addition:
To check if the result represents –17, we complement it and verify that it represents +17:
The 2’s complement of 11101111 is 00010001, which has the value +17.
Expected
Carries
Discard overflow bit
The result is 10000001. To verify that it represents –127, we complement it and verify that we get +127. The complemented pattern is 01111111 which, in fact, has the value of 127.
LHS 000 0 0 0 0 001 0 0 0 0 010 1 0 0 1 011 1 0 0 1 100 0 1 0 1 101 0 1 0 1 110 0 0 0 0 111 0 0 1 1
Since LHS=RHS, the proposition is proved.
