Week 7 Discrete Math Homework

1.  Write each of the following base-10 integers in base-2 and base-16.
(a) 22    (b) 527    (c) 1234    (d) 6923

2. Do any one out of four. These numbers are all 4-bit patterns of two's complement representations of the integers from -8 to 7. Solve each problem (if possible), and then convert the problem and results to base 10 to check your answers. Watch for any overflow errors.
   0101         1101        0111        1101
+ 0001      + 1110      + 1000     + 1010 

3. Convert the following (32-bit) positive integers into the other three bases (decimal, binary, octal, and hexadecimal).
(a) Decimal: 33         (c) Octal: 020755
(b) Binary: 1100111   (d) Hexadecimal: EA5D

4. Do any one out of two. Convert the following negative (decimal) integers into three (32-bit) binary representations: signed binary, twos complement, and with a bias of 2³¹ - 1 = 2,147,483,647.
(a) –186   (b) -43,704

5. Do any one out of two. Convert the following fractions into single-precision (32-bit) floating point values with bits ordered as follows: sign-bit|8-bit exponent with bias (+127)|23-bit fraction. Also, list the result as an 8-digit hexadecimal value.
(a) 5/9   (b) 75/11