Chapter 2: Number Systems, Sign Representations, and Two's Complement

Question 1

What does “bit” stand for?

Answer 1

Binary Digit

Question 2

How many values can a bit have?

Answer 2

2 possible values (0 and 1)

Question 3

What does a byte consist of?

Answer 3

8 bits

Question 4

With n bits, how many possible values are there?

Answer 4

2^n possible values

Question 5

1 K values is how many bits? Possible values?

Answer 5

2^10 values (10 bits) = 1024 values

Question 6

1 Mega values is how many bits? Possible values?

Answer 6

2^20 (20 bits) = 1,048,576 values

Question 7

1 Giga values is how many bits? Possible values?

Answer 7

2^30 (30 bits) = 1,073,741,824 values

Question 8

What does ASCII stand for?

Answer 8

American Standard Code for Information Interchange

Question 9

ASCII is how many bits and values?

Answer 9

7 bits, 128 values

Question 10

What is the Positional Notation System?

Answer 10

(Number at Index) x (Base)^Index

Question 11

Can every possible integer value be converted from one base to another?

Answer 11

Yes

Question 12

Can every possible fractional value be converted from one base to another?

Answer 12

No

Question 13

Describe binary multiplication

Answer 13

Choose one number as the multiplier and one as the multiplicand, for each digit in the multiplier, start from the rightmost digit, and write it top-down, shifting one left each time until all are done, then add (check notes for picture)

Question 14

What is range?

Answer 14

the variation between the smallest and largest possible values

Question 15

What is precision?

Answer 15

how well a number can be represented (how many significant digits)

Question 16

What is accuracy?

Answer 16

the difference between a representation and its actual value

Question 17

For Sign and Magnitude Representation, what does the leading bit represent?

Answer 17

Positive (0) or negative (1)

Question 18

For Sign and Magnitude Representation, how many representations of 0 are there?

Answer 18

2

Question 19

For Sign and Magnitude Representation, what is the range?

Answer 19

-2^(n-1) – 1 to 2^(n-1) – 1

Question 20

For Biased Representation, what is Excess-K?

Answer 20

shifting/adding the values by a certain number

Question 21

How do you get the original number using Biased Representation?

Answer 21

Subtract the excess

Question 22

How do you find the two’s complement of a binary number?

Answer 22

copy all zeros from the right until a one is reached, keep the one, flip all remaining bits

Question 23

For the Time example of Two’s complement, how do you find the two’s complement of a number?

Answer 23

the two’s complement of any number is 24 – (the number)

Question 24

What are the three important properties of Two’s Complement numbers?

Answer 24

• One unique zero
• Most-significant bit is the sign bit
• Range: -(2^n-1) to (2^n-1) – 1

Question 25

When will arithmetic overflow never occur?

Answer 25

When adding a positive number to a negative number

Question 26

How can you tell arithmetic overflow has occurred?

Answer 26

When the carry-in bit does not equal the carry-out bit after the addition has been completed

Question 27

Shifting to the right means

Answer 27

Dividing by 2

Question 28

Shifting to the left means

Answer 28

Multiplying by 2

Question 29

Write out the hexadecimal base system and the corresponding binary values

Answer 29

A

Question 30

Write out the octal base system and the corresponding binary values

Answer 30

A

Question 31

Write out the ranges of the following systems and the numbers of zeros they have: 2’s complement, signed-magnitude, Unsigned

Answer 31

• Unsigned (1 zero) : 0 to 2^(n) – 1
• Signed and Magnitude (2 zero) : -2^(n-1) – 1 to 2^(n-1) – 1
• 2’s Complement (1 zero) : -2^(n-1) to 2^(n-1) – 1

Question 32

Write out the possible values from 1 bit to 9 bits

Answer 32

A