Data representation

Question 1

how many bits are in 1 byte?

Answer 1

8

Question 2

how would you represent an unsigned integers in a n bit number?

Answer 2

raise 2 to the power of n - 1 finds the range of the possible numbers. (2^4 - 1 = 15 [0:16 = 16 different numbers)

Question 3

how to convert a number from base b to base 10?

Answer 3

multiply each number in the base b by base b to the power of the position of the number in the number and total it up (e.g.1234^5 –> ?^10 = 1 * 5^3 + 2 5^2 + 3^5^1 + 45^0

Question 4

how to convert a number from base 10 to base b?

Answer 4

divide the number by base b and put the remainders in the number starting from right to left, and keep dividing the result by base b until there are no more remainders

Question 5

how to convert a number from base b to base c?

Answer 5

you would convert it from base b to base 10, and then from base 10 to base c

Question 6

what do MSB and LSB refer to?

Answer 6

MSB refers to the most significant bit (far left digit) and LSB refers to the least significant bit (far right bit)

Question 7

what is 6 in binary

Answer 7

0110

Question 8

what is C in binary

Answer 8

1100

Question 9

how to convert a hex to a decimal?

Answer 9

use the positional number system to multiply out each digit in the number by 16 to the power of n-1

Question 10

how to convert a decimal to a binary number

Answer 10

divide decimal value by 2 until the value is 0, right remainders in the number from right to left

Question 11

how to convert a binary number to octal

Answer 11

look @ the table and which value aligns with what binary number

Question 12

how to convert an octal number into binary

Answer 12

write down the 3-bit binary code for each octal digit

Question 13

how to convert a binary number to a hexadecimal?

Answer 13

group into 4 starting at the LSB and correlate each 4-bit binary code into either a number or a letter in hex

Question 14

how to convert a hexadecimal to a binary number?

Answer 14

write down the 4-bit binary code for each hex digit

Question 15

how can you tell if a number is positive or negative in signed magnitude

Answer 15

look for the sign bit in the MSB: if it is 0, its + but if its 1, its -

Question 16

how to do one’s complement

Answer 16

invert the given number

Question 17

how to do two’s complement

Answer 17

invert the given number, add one

Question 18

how to do a logical right shift

Answer 18

move bits to the —> , same order, throw away the bit that comes off the LSB and introduce a 0 into the MSB

Question 19

how to do a logical left shift

Answer 19

move bits to the <—-, throw away the bit that pops off the MSB and tack on a 0 to the LSB

Question 20

how to do an arithmetic right shift

Answer 20

move the bits to the —>, throw away the bit that pops off, and reproduce the original MSB

Question 21

how to do an arithmetic left shift

Answer 21

move bits to the <—, throw away the bit that pops off the MSB and introduce a 0 into the LSB

Question 22

how to do a rotate left

Answer 22

move bits to the <—, put the bits that pop off the MSB into the LSB

Question 23

how to do a rotate right

Answer 23

move bits to the —>, put the bit that pops off the LSB into the MSB

Question 24

what does 2^-1 equal to?

Answer 24

negative exponent means its numerator: 1/2

Question 25

how would you find out the binary code of fractions from a given decimal value?

Answer 25

split the value into 2 parts: integer + fractional part. find the binary representation of the integer part by repeatedly divide the value and do the same for the fractional part but repeatedly multiply the value until you reach 0 as a product.