Question

Please show all the work with details.

I. CONVERSION FROM DECIMAL 1. Convert 879, to binary base-2), show work. 2. Convert 110710 to binary (base-2). show work

Answer 1

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1)
Divide 879 successively by 2 until the quotient is 0
   > 879/2 = 439, remainder is 1
   > 439/2 = 219, remainder is 1
   > 219/2 = 109, remainder is 1
   > 109/2 = 54, remainder is 1
   > 54/2 = 27, remainder is 0
   > 27/2 = 13, remainder is 1
   > 13/2 = 6, remainder is 1
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1101101111
So, 879 of decimal is 1101101111 in binary
Answer: 11011011

2)
Divide 1107 successively by 2 until the quotient is 0
   > 1107/2 = 553, remainder is 1
   > 553/2 = 276, remainder is 1
   > 276/2 = 138, remainder is 0
   > 138/2 = 69, remainder is 0
   > 69/2 = 34, remainder is 1
   > 34/2 = 17, remainder is 0
   > 17/2 = 8, remainder is 1
   > 8/2 = 4, remainder is 0
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10001010011
So, 1107 of decimal is 10001010011 in binary
Answer: 10001010

3)
Divide 879 successively by 16 until the quotient is 0
879/16 = 54, remainder is 15
54/16 = 3, remainder is 6
3/16 = 0, remainder is 3
Read remainders from the bottom to top as 36F
Answer: 36F

4)
Converting 11001101 to decimal
11001101
=> 1x2^7+1x2^6+0x2^5+0x2^4+1x2^3+1x2^2+0x2^1+1x2^0
=> 1x128+1x64+0x32+0x16+1x8+1x4+0x2+1x1
=> 128+64+0+0+8+4+0+1
=> 205
Answer: 205

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