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PLEASE SHOW MATH OF IT ALL Given n bits, how many signed numbers can be represented...

PLEASE SHOW MATH OF IT ALL

  1. Given n bits, how many signed numbers can be represented using the sign-and-magnitude method, the ones’ complement method, and the two’s complement method, respectively? (5 points)
  1. Number conversion (2.5 x 22 = 55 points)
  1. Convert the following unsigned binary numbers to decimal:

11111

101

  1. Convert the following decimal numbers to binary:

111

35

  1. Convert the following octal numbers to binary:

1111

731

  1. Convert the following unsigned binary numbers to octal:

101010111001

1001

  1. Convert the following decimal numbers to octal:

512

127

  1. Convert the following octal numbers to decimal:

101

2345

  1. Convert the following unsigned binary numbers to hexadecimal:

1010001001001111

1000110011111

  1. Convert the following hexadecimal numbers to binary:

abcdef

3A2B

  1. Convert the following decimal numbers to hexadecimal:

1111

13579

  1. Convert the following hexadecimal numbers to decimal:

bdef

FACE

  1. Convert the following numbers as required:

435 to base-3

2C516 to base-4

  1. Fraction conversion (2.5 x 8 = 20 points)
  1. 0.312510 to octal
  2. 3.62510 to binary
  3. 2.054687510 to hexadecimal
  4. 0.2EC516 to decimal
  5. 0.10112 to decimal
  6. 0.1011012 to hexadecimal
  7. 0.010111012 to octal
  8. 3.5728 to binary
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Homework Answers

Answer #1

Question 1) Convert the following unsigned binary numbers to decimal:

11111

Answer: 31

Explanation: 20 + 21 + 22 + 23 + 24 = 31

-------------------------

101

Answer: 5

Explanation: 20 + 22 = 5

-------------------------

Question 2) Convert the following decimal numbers to binary:

111

Answer: 110 1111

Explanation:

-------------------------

35

Answer: 10 0011

Explanation:

-------------------------

Question 3) Convert the following octal numbers to binary:

1111

Answer: 10 0100 1001

Explanation:

Write each octal number using 3 bits

1 = 001

Write it 4 times: 001 001 001 001

-------------------------

731

Answer: 1 1101 1001

Explanation:

7 = 111

3 = 011

1 = 001

Together = 111 011 001

-------------------------

Question 4) Convert the following unsigned binary numbers to octal:

101010111001

Answer: 5271

Explanation:

Group 3 bits at a time from last and write equivalent decimal number

101 010 111 001

5 2 7 1

-------------------------

1001

Answer: 11

Explanation:

1 001

1 1

I answered 8 sub parts for you but please post only 4 sub parts at a time as per the policy of Chegg.

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