Created 06/13/03; revised 08/21/15

# on Binary Addition and Two's Complement

Instructions: For each question, choose the single best answer. Make your choice by clicking on its button. You can change your answers at any time. When the quiz is graded, the correct answers will appear in the box after each question.

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 ```

```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
```

 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
```

 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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