Representing Numbers

Question 1

What are the steps to convert binary to decimal?

Answer 1

Going from left to right assign 2^0 then 2^1,2^2 and so on

Then multiply the number (either 1 or 0) by the associated base two power

Add them up

Question 2

What is 1010 in decimal?

Answer 2

(1 x 2^3) + (0 x 2^2) + (1 x 2^1) + (0 x 2^0)
= 8 + 0 + 2 + 0
=10

Question 3

How does the subtraction method work for converting decimal to binary?

Answer 3

Find the highest base 2 number that is less than the number you are trying to convert and subtract it

Repeat the process

Use a 1 for the base 2 power than you subtracted and a 0 for the ones you didn’t use

Question 4

Use the subtraction method to convert 75 to binary.

Answer 4

75-2^6 = 11

11-2^3 = 3

3-2^1 = 1

1-2^0 = 0

1001011

Question 5

How does the division method work to convert decimal to binary?

Answer 5

Divide the number by two

If it ends with 0.5 the remainder is 1, if it’s a whole number the remainder is 0

Read the remainders from the most significant bit to the least significant bit (from last division to first division)

Question 6

Use the division method to convert 75 to binary.

Answer 6

75/2= 37 R1
37/2= 18 R1
18/2= 9 R0
9/2= 4 R1
4/2= 2 R0
2/2=1 R0
1/2=0 R1

1001011

Question 7

How can you tell which is the MSB and LSB when converting decimal to binary?

Answer 7

MSB is at the bottom, last division you do

LSB is at the top, first division you do

Question 8

How can you convert decimal numbers to hexadecimal?

Answer 8

Divide the number you are trying to convert by 16

Use the integer as your next number and for the remainder multiply the decimal part by 16

Repeat until you hit 0

Take the remainders, convert them to hexadecimal, and read from MSB to LSB (bottom to top)

Question 9

Convert 479 to hexadecimal.

Answer 9

479/16 =29.9875=29 R15
29/16= 1.8125 =1 R 13
1/16= 0.0625 =0 R 1

15–>F
13–>D
1–> 1

1DF

Question 10

How can you convert hexadecimal to decimal?

Answer 10

Going from right to left label each number with 16^0, 16^1… and so on

Multiply that base 16 number by the number it’s assigned to

Add them up

Question 11

What is 23E in decimal?

Answer 11

(2 x 16^2) + (3 x 16^1) + (14 x 16^0)
= 512 + 48 + 14
=574

Question 12

If you are trying to convert a hexadecimal number that has decimals to decimal how would you do that?

Answer 12

Same thing but label the numbers to the right of decimal 16^-1, and so on

Question 13

How can you convert hexadecimal to binary?

Answer 13

Assign each hexadecimal number a decimal number

Convert the decimal number to binary

Put them together in the order the original numbers are

Question 14

Convert A9 to binary.

Answer 14

A=10
9=9

10-2^3=2-2^1
= 1010

9-2^3= 1-2^0
= 1001

10101001

Question 15

How can you convert binary to hexadecimal?

Answer 15

Seperate into groups of 4

Convert to decimal

Assign the decimal numbers hexadecimal numbers

Put together in right order

Question 16

What is 10110111 is hexadecimal?

Answer 16

1011 = 8+2+1=11
0111= 4+2+1= 7

11–>B
7–> 7

B7

Question 17

When converting binary to hexadecimal, what do you do if it doesn’t break into groups of four?

Answer 17

Add however many zeros in front of the binary number to make it equal to 4

Ex. 1011101010 turns into 001011101010

Question 18

How to convert to negative number in binary using 2 complement?

Answer 18

Replace every 1 with 0 and every 0 with 1

Then add one to that number