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missbossyy

Member

Registered: 2008-02-01

Posts: 38

binary

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

173
296
999
107
200
B. Convert the following Base 2 (binary) numbers to base 10 (decimal):

110011
1001111
11111111
11101
1010101
C. Add the following Base 2 (binary) numbers, submit the binary answer:

110001 + 111
1111 + 100
1001 + 101
101 + 101
100 + 1100
D. Subtract the following Base 2 (binary) numbers, submit the binary answer:

1001 - 101
10111 - 101
11011 - 100
1100 - 101
1000 - 1

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: binary

To convert from decimal to binary, express the decimal number as a sum of powers of 2. Thus, for 173, the last power of 2 before it is 128 = 2[sup]7[/sup]. So 173 = 128 + 45. Now express 45 as a sum of the powers of 2. The last power of 2 before 45 is 32 = 2[sup]5[/sup]. So 45 = 32 + 13. Continue doing this and you should get 173 = 128 + 32 + 8 + 4 + 1 = 2[sup]7[/sup] + 2[sup]5[/sup] + 2[sup]3[/sup] + 2[sup]2[/sup] + 2[sup]0[/sup]. Hence

Converting from binary to decimal is easier. Take 110011. You start with the digit on the extreme right and multiply that by 2[sup]0[/sup] = 1. Then you move to the left, multiplying each digit by successive powers of 2. So 110011 is 1×2[sup]5[/sup] + 1×2[sup]4[/sup] + 0×2[sup]3[/sup] + 0×2[sup]2[/sup] + 1×2[sup]1[/sup] + 1×2[sup]0[/sup], i.e.

Now you should be able to do the rest.

missbossyy

Member

Registered: 2008-02-01

Posts: 38

Re: binary

thanks!