Quiz 1

1. Convert the octal number A into the corresponding bases. Assume that A is unsigned. When you type your answer, the prefixes are optional.

A=0o260

Hexadecimal:

8-bit Binary:

• Answer

  Hex: (B0)16

  Binary: 10110000

3. A is an octal number being represented as a 8-bit 2's complement number. Is the 2's complement value positive or negative?

A = 571

• Answer

  Positive ((571)8 = (101111001)2, truncate the left-most bit to get 8 bits. Within the new number, the MSB is 0, and so the number is positive.)

5. Fill in the blank in the below statement to satisfy the equation. Assume all numbers are 8-bit. Please give your answer in decimal.

   0b10111011 & ~( 1 << ? ) = 0b10101011

   • Answer

     10111011

     & 11101111

     =10101011

     ~11101111= 00010000 = (16)10

     (16)10 = 1 << 4

     —> 0b10111011 & ~( 1 << 4 ) = 0b10101011

6. Fill in the below statement to satisfy the equation. Assume all numbers are 8-bit. Please give your answer in 8-bit binary.

   (0b10101010 ^ ? ) = 0b11001010

   • Answer

     10101010

     ^ 01111101

     = 11010111

7. Fill in the below statement to satisfy the equation. Assume all numbers are 8-bit. Please give your answer in hexadecimal.

   0b11100101 << (? >> 0x2) = 0b11001010

   • Answer

     11100101

     left shift by 1

     =. 11001010

     0x4 >> 0x2 = 1

     —> 0b11100101 << (0x4 >> 0x2) = 0b11001010

7. What could this IEEE number represent based on the given information?

   0 ________ 00001110101010000010010

   • Answer

     A positive number or NaN

8. What could this IEEE number represent based on the given information?

   0 00000000 ________________________________

   • Answer

     either 0 or a non-normalized number

9. What is the result obtained by adding the following two 5-bit unsigned binary numbers? Write your answer in 5-bit unsigned binary (ignoring carry-out and do not include spaces in between)

   11101 + 01110

   The answer for 11101 + 01110 in 5-bit unsigned binary is:

   In decimal is:

   • Answer

     5-bit unsigned binary: 01011

     Decimal: 43

     The answer overflows since it is larger than 31, the biggest number allowed in a 5 bit binary.

12. What is the result obtained by adding the following two 2's complement 5-bit binary numbers? Write your answer in 2's complement 5-bit binary (ignoring carry-out, and do not include spaces in between).

13. What is the result obtained by subtracting the following two 2's complement 5-bit binary numbers? Write your answer in 2's compliment 5-bit binary (ignoring carry-out and do not include spaces in between)

    10100 - 01000

    • Answer

      01100

      -20

      Overflow since carry-in is 0 and carry-out is 1. Also the decimal is larger than -16, the biggest negative number allowed in a 5-bit binary.

16. Given the following truth table, determine what the missing operator is in the corresponding boolean expression:

OUT = (A ^ ~B)___C

• Answer

  Missing Operator: &

17. Using DeMorgan’s Law, match the answer choices below to the equivalent logical expressions

    A | (B | ~C)

    • Answer

      A | ~(~B & C)

      ~ (~ A & ~(~B & C))

    A & (~B | ~C)

    • Answer

      A & ~(B & C)

      ~(~A | ~(~B | ~C))