Bits Manipulation

Question 1

How to remove the lowest set bit in x?

How to extract the lowest set bit in x?

Answer 1

How to remove the lowest set bit in x?

x & (x - 1)

How to extract the lowest set bit in x?

x & ~(x - 1)

Question 2

print(bin(4))

Answer 2

0b100
2 ** 2

Question 3

print(bin(8))

Answer 3

0b1 000
2 ** 3

Question 4

print(bin(16))

Answer 4

0b10 000
2 ** 4

Question 5

print(bin(32))

Answer 5

0b100 000
2 ** 5

Question 6

print(bin(64))

Answer 6

0b1000 000
2 ** 6

Question 7

print(bin(128))

Answer 7

0b10 000 000
2 ** 7

Question 8

print(bin(256))

Answer 8

0b100 000 000
2 ** 8

Question 9

print(bin(512))

Answer 9

0b1 000 000 000
2 ** 9

Question 10

print(bin(1024))

Answer 10

0b10 000 000 000
2 ** 10

Question 11

2 ** 5

Answer 11

32

Question 12

2 ** 6

Answer 12

64

Question 13

2 ** 7

Answer 13

128

Question 14

2 ** 8

Answer 14

256

Question 15

2 ** 9

Answer 15

512

Question 16

hex_num = “0xF”
decimal_num = int(hex_num, 16)
binary_num = bin(decimal_num)
print(binary_num)

What does this print out?

Answer 16

print(binary_num) # Output: ‘0b1111’

Question 17

num = hex(0b111)
print(num)

Answer 17

‘0x7’

Question 18

num = hex(0b11)
print(num)

Answer 18

‘0x3’

Question 19

num = hex(0b1111)
print(num)

Answer 19

‘0xf’

Question 20

num = hex(0b11111)
print(num)

Answer 20

‘0x1f’

Question 21

decimal = -1
What’s the 8-bit Two’s Complement of decimal?

Answer 21

8-bit Two’s Complement of -1 = 1111 1111

8-bit Two’s Complement of 1 = 0000 0001

只有2的几次方的数 正数和负数的significant digit都一样 其他digit 都相反

Question 22

decimal = -2
What’s the 8-bit Two’s Complement of decimal?

Answer 22

8-bit Two’s Complement of -2 = 1111 1110

8-bit Two’s Complement of 2 = 0000 0010

只有2的几次方的数 正数和负数的significant digit都一样 其他digit 都相反

Question 23

decimal = -4
What’s the 8-bit Two’s Complement of decimal?

Answer 23

8-bit Two’s Complement of -4 = 1111 1100

8-bit Two’s Complement of 4 = 0000 0100

只有2的几次方的数 正数和负数的significant digit都一样 其他digit 都相反

Question 24

decimal = -128
What’s the 8-bit Two’s Complement of decimal?

Answer 24

8-bit Two’s Complement of -128 = 1000 0000

8-bit Two’s Complement of 128= 1000 0000

只有2的几次方的数 正数和负数的significant digit都一样 其他digit 都相反

Question 25

current_bit &1
current_bit &0
current_bit ^ 1
current_bit ^ 0

What do these do to the current bit?

Answer 25

current_bit &1 = current bit stays the same
current_bit &0 = current bit gets erased
current_bit ^ 1 = flips the current bit
current_bit ^ 0 = current bit stays the same

Question 26

What happens with XOR?
a ^ b = c

a, b are binary bits

Answer 26

c = 0 when a == b
c = 1 when a != b

Question 27

With 2’s complement, -x = ________ ?

Answer 27

-x = ~x + 1
~x = -x - 1

Question 28

With 2’s complement, ~x is ?

Answer 28

~x = -x -1

Question 29

We have an integer x,
how can we convert it to -x using binary operations?

Answer 29

1. subtract 1 from x
2. flip each bit of 1

x = 0001
x - 1 = 0000
flipped x - 1 =1111 = -1