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Binary Conversion Problems and Solutions

Convert decimal numbers to binary, convert binary numbers to decimal, perform binary addition and subtraction. Understand two's complement. Solve and explain binary arithmetic problems step by step.

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Binary Conversion Problems and Solutions

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  1. Assignment 4 Sample problems

  2. Convert the following decimal numbers to binary. 8 920

  3. Convert the following decimal numbers to binary. 8 =>1000 920 =>1110011000

  4. How can we get ? 8 => 8*1= 23 =>1000 920 =>512*1+256*1+128*1+16*1+8*1 => 29 +28 +27 +24 +23 =>1110011000

  5. Convert the following Binary numbers to Decimal. 110100 100110011

  6. Convert the following Binary numbers to Decimal. 110100 =>52 100110011 =>307

  7. How can we get ? 110100 => 1* 25 +1*24 +1*22 =52 100110011 =>1* 28 +1*25 +1* 24+1* 21+1* 20 = 307

  8. Add the following binary numbers. Express your answers in binary. 101+011=? 11010+10001=?

  9. Add the following binary numbers. Express your answers in binary. 101+011=1000 11010+10001=101011

  10. How can we get ? 101+011 => 1 0 1 + 0 1 1 => 1 0 0 0 11010+10001 => 1 1 0 1 0 + 1 0 0 0 1 => 1 0 1 0 1 1

  11. Subtract the following binary numbers. Express your answers in binary. 101-001=? 11010-01001=?

  12. Subtract the following binary numbers. Express your answers in binary. 101-001=100 11010-01001=10001

  13. How can we get ? 101-001 => 1 0 1 - 0 0 1 => 1 0 0 11010-01001 => 1 1 0 1 0 - 0 1 0 0 1 => 1 0 0 0 1

  14. Is this statement True or False? If I have an 8-bit system, 10111001 + 00110000 will result in overflow. 

  15. Is this statement True or False? If I have an 8-bit system, 10111001 + 00110000 will result in overflow.  False

  16. How can we get ? • 10111001 + 00110000 • 10111001 + 00110000 • 11101001 The result is still 8-bit, so the answer is False

  17. Provide the two's complement of the following 8-bit numbers. 01001110 10010010

  18. Provide the two's complement of the following 8-bit numbers. 01001110 => 10110010 10010010 => 01101110

  19. How can we get ? 1: 01001110 => 10110001 (invert bits) + 00000001 (add one) => 10110010 2: 10010010 => 01101101 (invert bits) + 00000001 (add one) => 01101110

  20. Consider the Christmas lights circuit (with states) described in class.  Let these be the expressions for the next states. • A: not A • B: A and B

  21. Fill in the table with True or False where appropriate.

  22. Fill in the table with True or False where appropriate.

  23. The “period” of a pattern is the number of steps it takes before the pattern repeats. What is the period of this pattern?

  24. The “period” of a pattern is the number of steps it takes before the pattern repeats. What is the period of this pattern? 2

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