Q1.8 - Scientific Notation in Binary, Floating Point Numbers

1. Convert these decimals to binary.

  1. 3.375

  2. 67.625

  3. 73.9375

  4. 29.6875

  5. 3.71875

  6. 43.4375

  7. 25.5625

  8. 13.21875

2. Take these binary numbers and write them in binary scientific notation.

  1. 10000

  2. 11000001

  3. 10101000000

  4. 111010000000

  5. 1101101000

  6. 1010110000000000

  7. 0.00000101

  8. 0.000001011

  9. 0.00000011110

  10. 0.00000000011011

  11. 110.101

  12. 1000.0011

  13. 11011.0001

  14. 11011.001011

3. Take these decimal numbers, convert them to binary and write them in binary scientific notation.

  1. 8

  2. 64

  3. 256

  4. 16

  5. 25

  6. 36

  7. 41

  8. 300

4. Take these decimal numbers, convert them to binary and write them in binary scientific notation.

  1. 9.375

  2. 24.875

  3. 6.5

  4. 12.625

  5. 1.25

  6. 19.34375

  7. 5.3125

5. What is the matissa of each number? What is the exponent (characteristic)? (these are decimal)

  1. 1.223 X 10^23

  2. 4.56 X 10^-23

  3. -9.234 X 10^99

  4. -8.23 X 10^-23

6. What is the matissa of each number? What is the exponent (characteristic)? (these are binary)

  1. 1.011 X 2^23

  2. -1.0111 X 2^45

  3. 1.1101 X 2^-87

  4. -1.100101 X 2^-32

7. Why is it important that the floating point number be expressed in binary scientific notation? Does it need to be in scientific notation?

8. Why do we need to keep the sign bits separate? Why can’t we just include them in the scientific notation?

9. Write these binary numbers in floating point form.

1 bit Matissa Sign | 1 bit Chara Sign | 7 bit chara | 23 bit mantissa

  1. 1100000000000

  2. 10110000000000

  3. 110000001000000

  4. -11000000

  5. -11010111

  6. -1110000111

  7. 0.00000011

  8. 0.00000001101

  9. 0.000000101011

  10. -0.000000101

  11. -0.000010101

  12. -0.000001011

10. Write these decimal numbers in floating point form

1 bit Matissa Sign | 1 bit Chara Sign | 7 bit chara | 23 bit mantissa

  1. 100

  2. -124

  3. -15

  4. 16

  5. 345

  6. -989

  7. 123

11. Write these decimal numbers in floating point form

1 bit Matissa Sign | 1 bit Chara Sign | 7 bit chara | 23 bit mantissa

  1. 1792

  2. 0.00585

  3. 0.09375

  4. 52

  5. -0.109375

  6. -704

  7. -160

  8. -0.34375