Binary Number Homework Help?

Question

Can someone help and translate these to binary?

54-

33-

12-

85-

93-

45-

71-

22-

****SERIOUS ANSWERS ONLY****

Answer 1

I've given a "thumbs-up" to the suggestion to divide and keep track of remainders, but you need to remember one step that wasn't shown: when you get to a 1, you should divide that by 2 and get a remainder of 1. Example (from your problems):

85 ÷ 2 = 42 r. 1

42 ÷ 2 = 21 r. 0

21 ÷ 2 = 10 r. 1

10 ÷ 2 = 5 r. 0

5 ÷ 2 = 2 r. 1

2 ÷ 2 = 1 r. 0

1 ÷ 2 = 0 r. 1

Reading the remainders, backwards, gives 1010101 as the binary expression for decimal 85. But you need that last 1 to get it right!

Answer 2

Sure, easy

you have to remember the following

2 to the first power is 2

2 to the second power is 4

2 to the third power is 8

2 to the fourth power is 16

2 to the fifth power is 32

2 to the sixth power is 64

54 is between 2 to the fifth and 2 to the sixth

so

2 to the fifth plus 22

22 is 2 to the fourth plus 6

6 is 2² + 2

and 2 is 2 to the first power

so 54 =

2 to the fifth plus

2 to the fourth plus

2² plus

2 to the first

which in binary is

110110

1 for the fifth

1 for the fourth

0 for the third

1 for the second

1 for the first

and

0 for the zero

you can do the rest in the same fashion

Hope that helps

Answer 3

Want to know a quick way? =P

Simply keep dividing it by 2 and keep track of the remainders.

54 ÷ 2 = 27 ---> Remainder 0

27 ÷ 2 = 13 ---> 1

13 ÷ 2 = 6 -----> 1

6 ÷ 2 = 3 ------> 0

3 ÷ 2 = 1 ------> 1

The answer is reading it backward from the last quotient and all the remainder. 54 = 110110 in binary.

Cool eh?

Let try another one.

33 ÷ 2 = 16 ---> Remainder 1

16 ÷ 2 = 8 ----> 0

8 ÷ 2 = 4 -----> 0

4 ÷ 2 = 2 -----> 0

2 ÷ 2 = 1 ------> 0

So 33 = 100001

^_____^ What do you think?

Answer 4

I'll do the first two for you and leave the rest for you.  

Here's how binary works. Each place in a binary number represents a power of 2.  Reading from RIGHT TO LEFT, we have 2^0, 2^1, 2^2, 2^3, etc.  

so the number 10 means 1 of the 2^1 and 0 of the 2^0.  That equals 1(2^1)+0(2^0) = 2

the number 1011 means 1(2^3)+0(2^2)+1(2^1)+1(2^0) =8+0+2+1=11.

Got it?

Ok. So to translate 54 into binary, we need to see what the biggest power of 2 that will go in it.  2^5=32.

What's left over is 22.  

What's the biggest power of 2 that goes into 22? 2^4=16.  

What's left over is 6.  

What's the biggest power of 2 that goes into 6? 2^2=4.  

What's left over is 2;

and the biggest power of 2 that goes into that is 2^1.

So in binary, 54 = 110110     [=1(2^5)+1(2^4)+0(2^3)+1(2^2)+1(2^1)+1(2...

Now to translate 33:

The biggest power that goes in is 2^5=32

what's left over is 1

the biggest power that goes in is 2^0=1

So in binary, 33 =100001

[=1(2^5)+0(2^4)+0(2^3)+0(2^2)+0(2^1)+1...

Answer 5

54-110110

33-100001

12-1100

85-1010101

93-1011101

45-101101

71-1000111

22-10110