# 23 - Twos Complement

1. Another method of representing signed numbers is two's complement. Most computers use this method to represent negative numbers.

FALSE

TRUE

2. With two's complement, the bit at the far left of the bit pattern - the most significant bit or MSB - is used to __________________

None of the above

indicate the magnitude or size of the number

indicate positive or negative

indicate the length of the binary sequence

FALSE

TRUE

4. A four-bit, positive, two's complement number could hold a maximum value of _________

8

6

7

5

5. 1111 in two's complement would be:

minus 3

minus 1

minus 2

zero

6. The number -8 would be represented in two's complement as:

1010

1110

1000

1111

7. Read the rules (below) for using two's complement for negative numbers. What is the missing step #4?
```#1:
Find the positive binary value for the negative number
you want to represent.

#2
Add a 0 to the front of the number, to indicate that it is positive.

#3
Invert or find the complement of each bit in the number.

#4
__________________________________```

None of the above

Invert th e bits again and remove the leading 1

8. What should happen in step 3? (to convert -1 into twos complement)
```Find -1 using two's complement numbers
=======================================

Step 1: 1 = 001
Step 2: Adding 0 to the front becomes 0001
Step 3: .................................
Step 4: Add 1 = 1111 (-8 + 4 + 2 + 1 = -1)```

Invert all the bits and add 1 which gives 11101

None of the above

Inverted' becomes 1110

Reverted becomes 1111000

9. Look at the following calculation to convert -4 into two's complement. Is it correct? Which statement is true?
```Find -4 using two's complement numbers
======================================

4 = 100
Adding 0 to the front becomes 1000
'Inverted' becomes 0001
Add 1 = 0010 = -4```

The step that adds 1 is incorrect - in this case, it should add +4

The step that inverts the bits is incorrect

The calculation is correct

The step which adds a 0 has been done wrong. It should be 0100

10. What is the two's complement four bit binary number 0001?

1

3

4

2

11. What is the two's complement four bit binary number 0110?

positive 3

minus 3

positive 6

minus 6

12. What is the two's complement four bit binary number 1011?

minus 3

positive 5

minus 5

positive 3

13. What is +2 in two's complement binary? (four bits)

2 would be 0010

2 would be 1100

2 would be 0011

2 would be 1110

14. Positive 2 in two's complement binary (using eight bits) would be 01110010

FALSE

TRUE

15. How would you represent the positive integer 256 in eight bits (two's complement format)?

ERROR: input requires 10 bits; 8 bits were specified

16. Why is it not possible to represent the number 54 in four bits (two's complement)?

54 is not an odd number, which presents difficulties in two's complement

54 would require 10 bits

It is possible to represent in four bits

54 would require 7 bits

17. The following representation is minus 74 in:
`11001010`

sign and magnitude

two's complement

ASCII

None of the above

18. The following number is -74 in two's complement: 10110110

TRUE

FALSE

19. The following calculation that converts -9 into two's complement is correct?
```-9
-128	64	32	16	8	4	2	1
1	1	1	1	0	1	1	1

-128+64+32+16+4+2+1=-9```

FALSE

TRUE

20. Is this calculation, that converts -105 to two's complement, correct?
```-105
-128	64	32	16	8	4	2	1
1	1	0	1	0	1	1	1
-128+64+ 16+4+2+1=-105```

No - there should be no 1 under the 64

No - there should be no 1 under the 16

Yes

It is incorrect because -105 cannot be represented in just eight bits