Java Primitive Data Types and Base Conversion

1. Use repeated division/multiplication by 8 and a binary 3-digit lookup to convert the following numbers by hand, to binary, then to hexadecimal.
1. 88
   

   8| 88	Remainders	1308
   8| 11	0.	001 011 0002
   8|  1	3	0101 1000
   0	1	5816

    

2. 132
   

   8| 132	Remainders	2048
   8| 16	4.	010 000 1002
   8|  2	0	1000 0100
   0	2	8416

    

3. 132.456
   

   13210 = 2048		204.3518
   8 x 0.456 = 3.648	0.45610 » 0.3518	010 000 100.011 101 0012
   8 x 0.648 = 5.184	3	1000 0100.0111 0100 1000
   8 x 0.184 = 1.472	1	84.74816

    

4. 103
   

   8| 103	Remainders	1478
   8|  12	7.	001 100 1112
   8|    1	4	0110 0111
   0	1	6716

    

5. 10.1
   

   8| 10	Remainders	12.0638
   8|   1	2.	001 010.000 110 0112
   0	1	1010.0001 1001 1000
   8 x 0.1 = 0.8, 8 x 0.8 = 6.4, 8 x 0.4 = 3.2	0.063	A.19816

    

2. Convert the following binary number s to decimal, hex, and octal. Then convert each octal and hex number back to decimal.
1. 1010.0001100110011
   (2³ + 2¹) . (2^-4 + 2^-5 + 2^-8 + 2^-9 + 2^-12 + 2^-13) = 10.099975585938
   1 010.000 110 011 001 1 = 12.06314₈
   1010.0001 1001 1001 1 = A.1998₁₆
   12.06314₈ = (8¹ + 2×8⁰) . (6×8^-2 + 3×8^-3 + 8^-4 + 4×8^-5) = 10.099975585938
   A.1998₁₆ = (10×16⁰) . (16^-1 + 9×16^-2 + 9×16^-3 + 8×16^-4) = 10.099975585938
2. 1000011
   2⁶ + 2¹ + 2⁰  = 67
   001 000 011 = 103₈ = 8² + 3×8⁰ = 67
   0100 0011 = 43₁₆ = 4×16¹ + 3×16⁰ = 67
   
3. 10110000.001101001011
   2⁷ + 2⁵ + 2⁴ + 2^-3 + 2^-4 + 2^-6 + 2^-9 + 2^-11 + 2^-12 = 176.205810547
   010 110 000.001 101 001 011 = 260.1513₈ = 2×8² + 6×8¹ + 8^-1 + 5×8^-2 + 8^-3 + 3×8^-4 = 176.205810547
   
   1011 0000.0011 0100 1011 = B0.34B₁₆ = 11×16¹ + 3×16^-1 + 4×16^-2 + 11×16^-3 = 176.205810547
   
4. 1001001
   2⁶ + 2³ + 2⁰ = 73
   001 001 001 = 111₈ = 8² + 8¹ + 8⁰ = 73
   0100 1001 = 49₁₆ = 4×16¹ + 9×16⁰ = 73
   
3. Write the following numbers as Java bytes then convert the Java bytes to hexadecimal.
1. 123
   

   8| 123	Remainders	1738
   8|  15	3.	001 111 0112
   8|    1	7	0111 1011
   0	1	7B16

    

2. -123
   -(0111 1011) = 1000 0101 = 85₁₆
   
3. 8
   10₈ = 001 000 = 0000 1000 = 8₁₆
   
4. -8
   -(0000 1000) = 1111 1000 = F8₁₆
   
4. Write the following as Java integers, convert the Java word to hexadecimal.
1. 129
   0000 0000 0000 0000 0000 0000 1000 0001
   00000081₁₆
   
2. -129
   1111 1111 1111 1111 1111 1111 0111 1111
   FFFFFF7F₁₆
   
3. 12,500
   0000 0000 0000 0000 0011 0000 1101 0100
   0000030D4
   
4. -12,500
   1111 1111 1111 1111 1100 1111 0010 1100
   FFFFCF2C₁₆