1.1 - number systems 🔢

Question 1

which number is binary based on?

Answer 1

2

Question 2

which number is denary based on?

Answer 2

10

Question 3

which number is hexadecimal based on?

Answer 3

16

Question 4

how can numbers be converted from binary to denary?

Answer 4

by multiplying the 1-values with their headings and adding them up (eg. 1101 -> (18)+(14)+(02)+(11) = 8 + 4 + 1 = 13)

Question 5

how can numbers be converted from denary to binary?

Answer 5

by successively dividing them by 2 (eg. 120 / 2 = 60R0 / 2 = 30R0 / 2 = 15R0 / 2 = 7R1 / 2 = 3R1 / 2 = 1R1 / 2 = 0R1 -> 1111000)

Question 6

how can numbers be converted from binary to hexadecimal?

Answer 6

by splitting a binary number into fragments of 4 bits and then determining those fragments’ values (eg. 00110100 -> 1011 0100 -> 11 and 4 -> B4)

Question 7

how can numbers be converted from hexadecimal to binary?

Answer 7

by first converting the hexadecimal digits into 4-bit binary numbers and then combining them into a single 8-bit number (eg. 9D -> 9 and 13 -> 1001 1101 -> 10111101

Question 8

how are MAC addresses (hexadecimal network device identifiers) formatted?

Answer 8

as MM:MM:MM:SS:SS:SS or MM-MM-MM-SS-SS-SS (M = manufacturer ID, S = device serial number)

Question 9

what are some examples of manufacturer IDs in MAC addresses?

Answer 9

94:BF:2D (Apple), 9C:7B:EF (HP), A0:91:A2 (OnePlus)

Question 10

how are IPv4 addresses formatted?

Answer 10

as either xxx.xxx.xxx.xxx (denary) or xx.xx.xx.xx (32-bit hexadecimal)

Question 11

how are IPv6 addresses formatted?

Answer 11

as xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:xxxx (64-bit hexadecimal)

Question 12

what are hexadecimal error codes used for?

Answer 12

to identify randomly-generated memory locations (eg. E00 -> 1110 0000 0000)

Question 13

what do the hexadecimal numbers in HTML color codes stand for?

Answer 13

RGB values (eg. #FF0000 -> R255 G0 B0)

Question 14

what’s an overflow error?

Answer 14

when there are more bits in a binary value than a device can allow for (eg. generating a 33-bit binary value when the maximum number of bits is 32 causes an overflow error)

Question 15

how do logical shifts work?

Answer 15

they either multiply binary numbers by 2 (when done to the left) or divide them by that same number (when done to the right)

Question 16

what’s different in two’s compliment mode?

Answer 16

the leftmost bit determines the number’s sign (0 = positive, 1 = negative)

Question 17

how do you convert negative denary numbers into binary?

Answer 17

by writing the denary value’s positive counterpart in binary, inverting all the bits, and adding 1 to the result

Question 18

(C1) convert the denary number 98 into binary without using a calculator

Answer 18

01100010

Question 19

(C2) convert the non-two’s complement binary number 10010010 into denary without using a calculator

Answer 19

146

Question 20

(C3) convert the hexadecimal number E04 into binary without using a calculator

Answer 20

1110 0000 0100

Question 21

(C4) convert the binary number 0101 0101 into hexadecimal without using a calculator

Answer 21

55

Question 22

(C5) convert the hexadecimal number F4 into denary without using a calculator

Answer 22

244

Question 23

(C6) convert the denary number 39 into hexadecimal without using a calculator

Answer 23

27 because 39 in binary = 0010 1001

Question 24

(C7) logically shift the binary number 00100101 (37 in denary) to the left and work out its value without using a calculator

Answer 24

01001010 (74 in denary - the original value was multiplied by 2)

Question 25

(C8) convert the denary number -101 to two’s complement-format binary without using a calculator

Answer 25

+101 = 01100101 in binary so flipping the digits turns this into 10100110 and adding 1 turns this into the final answer of 10100111