binary numbers

missbossyy · 2008-02-01 11:54:30

Convert the following base 10 (decimal) numbers to base 2 (binary):

1. 173

2. 296

3. 999

Convert the following base 2 (binary) numbers to base 10 (decimal):

4. 110011

5. 1001111

6. 11111111

Add the following two base 2 (binary) numbers together:

7. 110001 + 111

8. 1111 + 100

John E. Franklin · 2008-02-01 12:07:55

#7. 110001 + 111
is the same as
110000 + 001 + 111

Wait, let's do something else similar to learn:
What is 7 + 3, it's ten!!
Okay 7 in binary is 111 and 3 in binary is 011, or 11 if you prefer.
Now let's add them up, knowing the answer must be 1010 since that is ten in binary.
You must know that 1 + 1 + 1 is 11 because that is 3 in binary.
You will need the 1 + 1 + 1 information when carrying the one.
Start on the right column.
I'll label the columns.
ABC
111
011 +
--------
Okay add C column: 1 + 1 = 10. Now break the 10 into the 1 for carry and 0 to write down.
The answer is currently: *0, where * stands for unknown digits, continue...
Add column B and add in the carry 1 too: 1 + 1 + 1 = 11, so write down a 1 and carry a 1.
Now the answer is: *10
Add column A and add in the carry 1 too: 1 + 1 + 0 = 10, so write down the 0 and carry the 1.
Now the answer is: *010
There are no more columns, so just write down the carry 1 now on the left of the number.
Answer = 1010
See 1010 is ten!! 7 + 3.

Last edited by John E. Franklin (2008-02-01 12:26:06)

missbossyy · 2008-02-01 12:10:55

please help me with 1, 2, 3 , 4, 5, 6 ASAP....my project is due in no time......

John E. Franklin · 2008-02-01 12:32:20

#5. 1001111 is about a hundred, but let's work on it...
1111 is fifteen because 1 + 2 + 4 + 8 is 15, the places go 8421, so add up the places.
Then the 00 is zero times 16 + 32, so that's just zero.
Then the 1 on the left is 64.
So 64 + 15 is answer, or seventy-nine.

missbossyy · 2008-02-01 12:32:32

Binary: 110011 Decimal: 51

Binary: 1001111 Decimal: 79

Binary: 11111111 Decimal: 255

so is this right for 4, 5, 6?

missbossyy · 2008-02-01 12:39:09

thanks u r helpying me i reallly really apericate it from my heart

John E. Franklin · 2008-02-01 12:40:49

#6. 11111111 is eight 1's in a row.
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 is answer, or 128 + 127 = 255 answer.
Another way to do it is:
Take the 1 on the left and double it to 2.
Then add in the 2nd 1 from the left, so 2 + 1 is 3, and double that: 6
Then add in the 3rd 1 from the left: 6 + 1 = 7, double = 14
Add 4th 1 in and double: 15 doubled is 30
Add 5th 1 in and double: 31 twice is 62
Add 6th 1 in and double: 62 + 1, double to 126.
Add the 7th 1 in and double: (126 + 1) times 2 makes 254
Add in the 8th 1 on the right of 11111111, so 254 + 1 is the answer, or 255.

mathsyperson · 2008-02-01 12:41:02

Binary: 110011 Decimal: 51
Binary: 1001111 Decimal: 79
Binary: 11111111 Decimal: 255
so is this right for 4, 5, 6?

Yeppers!

And for the first three, you need to write each number as a sum of powers of two.
For example, 173 = 128 + 32 + 8 + 4 + 1.

This is 2^7 + 2^5 + 2^3 + 2^2 + 2^0.

Count down from 7 until you get to 0, then write a 1 under each number whose power is in that sum.

76543210
10101101

And there's your answer. 173 in base 10 is 10101101 in base 2.

John E. Franklin · 2008-02-01 12:43:23

#4. is right!! because 3, 6, 12, 24, 48 + 3 = 51, hurray!!
#5. 64 + 15 is 79, hurray, you are right!!

missbossyy · 2008-02-01 12:46:35

omg! guys u r so helpful finally am getting this....yeay! i am so in love with this site.....

missbossyy · 2008-02-01 12:50:22

1. 10101101
2. 000100101000
3. 001111100111
is that right????????????

John E. Franklin · 2008-02-01 12:50:33

ten is 1010
a hundred is 64 + 36, and 36 is 32 + 4, 64 + 32 + 0×16 + 0×8 + 4 + 0×2 + 0x1
a hundred is 1's whereever the 64, 32, and 4 are.
a hundred is 1100100
Since ten is 1010, then if you put 11 in place of every 1, then you should get 30
because ten times 3 is 30.
1111 is 15 though, but 11110 is 30 Yeah!!

John E. Franklin · 2008-02-01 12:53:08

#1. I check answer: go Right to Left easy to check, 'cause 1248 16 32 64 way.
1 + 4 + 8 + 32 + 128 = 173 Yup!! You're right!

Last edited by John E. Franklin (2008-02-01 12:53:27)

John E. Franklin · 2008-02-01 12:55:59

#2. 296 okay, I'll check your number backwards again...
1 2 4, all zero, then 8 + skip 16 + 32 + skip 64 skip 128 + 256 plus 3 zeros you have on right do nothing though.
So 8 + 32 + 256 are the three ones, and that's 40 + 256 = 296 Yeah!! It's right.
There is another way to do this by dividing by 2 over and over or something too.

missbossyy · 2008-02-01 12:58:20

may God bless u with all happiness Franklin...
thanks for u r time man.

John E. Franklin · 2008-02-01 13:01:00

#3. 999, let's see... 1111100111 you think, uh...
the five one's in a row is 31 and then double that five times since there are 00111 after it.
So 31 × 2 × 2 × 2 × 2 × 2 = 62 dbl is 124 dubble is 248 duble is 496 duble is 8 under 1000
since 496 is 4 under 500.
Now add in the 3 ones at the end of the number.
111 is seven because 1 + 2 + 4 is 7.
So 8 under 1000 plus 7 is 999!! Yeah!!
You got it right!!

John E. Franklin · 2008-02-01 13:02:13

Thanks a lot!!
And there is another way to divide a number and use the remainder to
convert bases, but I would have to look it up or guess at it and try it.

pi man · 2008-02-01 16:34:48

This may be the method you're referring to. Convert 70 (decimal) to binary.

70 / 2 = 35 R0
35/2 = 17 R1
17/2 = 8 R1
8/2 = 4 R0
4/4 = 2 R0
2/2 = 1 R0
1/2 = 0 R1

You answer is the remainders reading upwards: 1000110

Works for converting to any number system: 949 to base 16:

949 /16 = 59 r5
59 / 16 = 3 r11 (hex B)
3 / 16 = 0 r3

949 (decimal) = 3B5

missbossyy · 2008-02-02 10:22:43

thanks!:):):):):):):):):):)

Math Is Fun Forum

#1 2008-02-01 11:54:30

binary numbers

#2 2008-02-01 12:07:55

Re: binary numbers

#3 2008-02-01 12:10:55

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#4 2008-02-01 12:32:20

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#5 2008-02-01 12:32:32

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#6 2008-02-01 12:39:09

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#7 2008-02-01 12:40:49

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#8 2008-02-01 12:41:02

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#9 2008-02-01 12:43:23

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#10 2008-02-01 12:46:35

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#11 2008-02-01 12:50:22

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