1 (Number Representation, Addition and Subtraction) (Part A) Specify whether an
ID: 3612857 • Letter: 1
Question
1 (Number Representation, Addition and Subtraction)(Part A) Specify whether an overflow can occur in the operations onthe incomplete 2’s comple-
ment numbers listed in the following table where the x’srepresent unknown values. Fill in the
blanks with a “Yes” if you think the correspondingoperation will generate an overflow; fill it in
with a “No”, otherwise.
Operations
Overflow? 011xx0x1 +1x1111x1
01x10xxx 100xxx1x
111xx1xx +1x1xx1x1
0x11x00x + 01x1x001
1x1x10xx 1xxxx1x1
(Part B) Decimal numbers are usually encoded in the BCD format. Forexample, 5710 can be
represented by two 4-bit BCD digits 0101 0111. To complete theaddition/subtraction operations
on these decimal numbers, a possible correction step might need tobe applied to the result to
attain the correct BCD code for the digit of the sum/differencebeing computed. The candidate
correction operations include the following:
A Do nothing
B Add 3
C Add 6
D Add 10
The table below contains several arithmetic operations on 1-digitBCD codes where the x’s
represent unknown values. For each case, fill in the box with theindex of the appropriate
correction operation.
Correction operation 0100 +0111 ?
0xxx 1xxx ?
xx1x +1xxx ?
01xx 00x1 ?
(Part C) If 1r3 =r2r2, what are the valuesfor the integers , and r? (Hint: perhaps
expanding the two sides of the given equation to a partial radix rrepresentation may help you
reason about this question more effectively.)
Operations
Overflow? 011xx0x1 +1x1111x1
01x10xxx 100xxx1x
111xx1xx +1x1xx1x1
Explanation / Answer
please rate - thanks please note-CRAMSTER rule is 1 question per post 1 (Number Representation, Addition and Subtraction)(Part A) Specify whether an overflow can occur in the operations onthe incomplete 2’s comple-
ment numbers listed in the following table where the x’srepresent unknown values. Fill in the
blanks with a “Yes” if you think the correspondingoperation will generate an overflow; fill it in
with a “No”, otherwise.
Operations
Overflow? 011xx0x1 +1x1111x1
YES for example 01111011+11111111 would give overflow
01x10xxx 100xxx1x YES high order bit 0-1 gives overflow, ignoringeverything else
111xx1xx + 1x1xx1x1 YES high order bit 1+1 gives overflowignoring everything else
0x11x00x + 01x1x001
NO because high order bits are0, couldn't have overflow
1x1x10xx 1xxxx1x1 NO because high order bit would be 1-1 nooverflow
(Part B) Decimal numbers are usually encoded in the BCD format. Forexample, 5710 can be
5710 =0101 0111 0001 0000 in BCD
represented by two 4-bit BCD digits 0101 0111 this is only 57. To complete the addition/subtractionoperations
on these decimal numbers, a possible correction step might need tobe applied to the result to
attain the correct BCD code for the digit of the sum/differencebeing computed. The candidate
correction operations include the following:
A Do nothing
B Add 3
C Add 6
D Add 10
The table below contains several arithmetic operations on 1-digitBCD codes where the x’s
represent unknown values. For each case, fill in the box with theindex of the appropriate
correction operation.
Correction operation 0100 +0111 ?
0xxx 1xxx ?
xx1x +1xxx ?
01xx 00x1 ?
(Part C) If 1r3 = r2r2, what are the values forthe integers , and r? (Hint: perhaps
expanding the two sides of the given equation to a partial radix rrepresentation may help you
reason about this question more effectively.)
Operations
Overflow? 011xx0x1 +1x1111x1
YES for example 01111011+11111111 would give overflow
01x10xxx 100xxx1x YES high order bit 0-1 gives overflow, ignoringeverything else
111xx1xx + 1x1xx1x1 YES high order bit 1+1 gives overflowignoring everything else
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