Created 06/13/03

# on Binary Addition and Two's Complement

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1. In the following one-bit wide addition, what are the result R and the carry, C?

    C0
     0
     1
    --
     R

A. C=0; R=0
B. C=0; R=1
C. C=1; R=0
D. C=1; R=1

2. In the following one-bit wide addition, what are the result R and the carry, C?

    C1
     0
     1
    --
     R

A. C=0; R=0
B. C=0; R=1
C. C=1; R=0
D. C=1; R=1

3. Which one of the following is done correctly?

A.
    0100
     0110
     0101
     ----
     1011
B.
    0100
     0110
     0101
     ----
     1111
C.
    0110
     0110
     0101
     ----
     1111
D.
    0101
     0110
     0101
     ----
     1001

4. Which one of the following is done correctly?

A.
    0100
     1110
     1001
     ----
     1001
B.
    0000
     1110
     1001
     ----
     0111
C.
    0111
     1110
     1001
     ----
     1001
D.
    1000
     1110
     1001
     ----
     0111

5. Perform the following addition:

    1100
    0101
    ----

A. 0001 with a carry out of the left column of 1
B. 0001 with a carry out of the left column of 0
C. 1001 with a carry out of the left column of 1
D. 1110 with a carry out of the left column 1

6. Here is a two's complement representation of an integer:

    0011 1001

What is the two's complement representation of the negation of the integer?

A. 1100 0110
B. 1011 1001
C. 1100 1110
D. 1100 0111

7. Here is a two's complement representation of an integer:

    1100 0111

What is the two's complement representation of the negation of the integer?

A. 1100 0110
B. 0011 1001
C. 0000 1110
D. 0100 0111

8. Here is a correctly performed addition:

    1100
     0100
     1110
     ----
     0010

What is true about overflow for this addition?

A. If the operands are regarded as unsigned binary, then the result shows no overflow. If the operands are regarded as two's complement binary, then the result shows no overflow.
B. If the operands are regarded as unsigned binary, then the result shows overflow. If the operands are regarded as two's complement binary, then the result shows no overflow.
C. If the operands are regarded as unsigned binary, then the result shows no overflow. If the operands are regarded as two's complement binary, then the result shows overflow.
D. If the operands are regarded as unsigned binary, then the result shows overflow. If the operands are regarded as two's complement binary, then the result shows overflow.

9. Here is a correctly performed addition:

    1000
     1100
     1010
     ----
     0110

What is true about overflow for this addition?

A. If the operands are regarded as unsigned binary, then the result shows no overflow. If the operands are regarded as two's complement binary, then the result shows no overflow.
B. If the operands are regarded as unsigned binary, then the result shows overflow. If the operands are regarded as two's complement binary, then the result shows no overflow.
C. If the operands are regarded as unsigned binary, then the result shows no overflow. If the operands are regarded as two's complement binary, then the result shows overflow.
D. If the operands are regarded as unsigned binary, then the result shows overflow. If the operands are regarded as two's complement binary, then the result shows overflow.

10. Say that there are two operands represented using the two's complement method:

    operand A = 0011 1010          operand B = 0110 1011

Which of the following uses of the binary addition algorithm shows the problem `A - B`?

A.
    0011 1010
    0110 1011
    ---------
B.
    1100 0110
    0110 1011
    ---------
C.
    0011 1010
    1001 0101
    ---------
D.
    1100 0101
    1001 0110
    ---------

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