#16 Negative Numbers, Fractions and Bitwise Operations

1. How do you know a number is negative if it is expressed in two's complement?

• A. The LSB is 1
• B. The LSB is 0
• C. The MSB is 1
• D. The MSB is 0

2. Which of the following describes sign and magnitude notation?

• A. The MSB has a value and a sign and there are two ways to represent zero
• B. The MSB has a sign but no value and there are two ways to represent zero
• C. The LSB has a sign and a value and there are two ways to represent zero
• D. The MSB has a value and a sign but there is only one way to represent zero

3. In which notation would the number 100010 represent the number -2?

• A. Sign and magnitude
• B. Two's complement
• C. Unsigned binary
• D. Floating point

4. How many different negative numbers can be represented as 4-bit two's complement integers?

• A. 8
• B. 16
• C. 15
• D. 7

5. Convert the sign and magnitude number 10101000 to denary

• A. -88
• B. -40
• C. 168
• D. -84

6. Two's complement is in use here. Calculate 011110001110 using binary subtraction and state your answer as an 8-bit two's complement binary integer

• A. 11110001
• B. 01110100
• C. 00101110
• D. 100101110

7. In normalised floating point binary, if there are 4 bits for the mantissa and 4 bits for the exponent, what is the largest positive number that can be written down?

• A. 11111111
• B. 01110000
• C. 01110111
• D. 10001111

8. How do you write the number -1 as a two's complement binary integer?

• A. The MSB must be 0 but thereafter it depends how many bits there are
• B. There are several ways to do it but the LSB must always be 1 (to make it odd) and the MSB must be 0
• C. The MSB must be 1 but thereafter it depends how many bits there are
• D. A continuous sequence of 1s only, of any length

9. Using an 8-bit mantissa and a 4-bit exponent, represent the number -25.5 in normalised floating point

• A. 1001101101
• B. 100110101011
• C. 010011010101
• D. 100110100101

10. Convert the normalised floating point number 101000101101 to a denary fraction given that it has an 8-bit mantissa and a 4-bit exponent

• A. -15/4
• B. -15/256
• C. -17/256
• D. -17/4