The document discusses how real numbers are represented in IEEE standard form using 32 bits divided into three sections - a sign bit, 8-bit exponent, and 23-bit number. It provides the 5 steps to convert a real number into its IEEE representation: 1) calculate the binary form, 2) normalize it, 3) set the sign bit, 4) store the exponent as an 8-bit binary after adding 127, and 5) store the remaining bits of the normalized form. It asks to represent 25.010 in this standard form.

1. 1.16
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
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2. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Goal
To be able to represent real numbers in IEEE standard
form.
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3. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
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4. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
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5. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Real Numbers are stored by a totally different method
from integers.
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6. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Real Numbers are stored by a totally different method
from integers.
Although many schemes are possible, we will explore a
scheme that is widely used and accepted by the IEEE
(Institute for Electrical and Electronic Engineering).
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7. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
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8. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Real numbers are stored as
32 bits (usually referred to as the type ‘float’) or
64 bits (usually referred to as the type ‘double’).
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9. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Real numbers are stored as
32 bits (usually referred to as the type ‘float’) or
64 bits (usually referred to as the type ‘double’).
For our discussions, we’ll use 32 bits
35.0
to represent a real number.
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10. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
The 32 bits are divided into 3 sections.
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11. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
The 32 bits are divided into 3 sections.
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12. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
sign
bit
The 32 bits are divided into 3 sections.
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13. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
sign e xponent
bit 8 bits
The 32 bits are divided into 3 sections.
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14. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
sign e xponent number
bit 8 bits 23 bits
The 32 bits are divided into 3 sections.
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35.0

15. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
sign e xponent number
bit 8 bits 23 bits
The 32 bits are divided into 3 sections.
This is the 1-8-23 pattern.
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16. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
sign
bit sign bit : 0 for a positive number, 1 for negative
The 32 bits are divided into 3 sections.
This is the 1-8-23 pattern.
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35.0

17. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
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18. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Steps to represent a number in IEEE standard form
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19. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
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20. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
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21. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
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22. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
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23. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
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24. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
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25. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 25.010 in IEEE standard
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

26. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

27. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02
2. normalize 11001.02
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
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28. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02
2. normalize 11001.02 1.1001 x 2 4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

29. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers this is similar to
scientific notation
except that we use
Represent 25.010 in IEEE standard powers of 2
1. 25.010 = 11001.02
2. normalize 11001.02 1.1001 x 2 4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
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30. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
we moved the
point 4 positions to
the left, so our
Represent 25.010 in IEEE standard
exponent is 4
1. 25.010 = 11001.02
2. normalize 11001.02 1.1001 x 2 4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

31. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02
2. normalize 11001.02 1.1001 x 2 4
3. set the sign bit
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

32. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 25.010
is a positive number
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

33. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 25.010
is a positive number
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

34. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit
4. store 4 in the exponent section
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

35. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0
Represent 25.010 in store standard
we want to IEEE
1. 25.010 = 11001.02negative and
both 1.1001 x 24
positive exponents
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit
4. store 4 in the exponent section
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
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36. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0
Represent 25.0store itIEEE standard
we’ll 10 in so that
it corresponds to the
1. 25.010 = 11001.02 1.1001 x 24
following table
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit00000000 -127
4. store 4 in the exponent section
00000001 -126
00000010 -125
… …
01111111 0 Steps to represent a number in IEEE standard form
10000000 1 1. calculate the binary form of the number
10000001 2 2. calculate the normalized binary form
10000010 3 3. set the sign bit
10000011 4 4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
… …
11111111 128
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37. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0
Represent 25.0store itIEEE standard
we’ll 10 in so that
it corresponds to the
1. 25.010 = 11001.02 1.1001 x 24
following table
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit00000000 -127
4. store 4 in the exponent section
00000001 -126
00000010 -125
… …
01111111 0 Steps to represent a number in IEEE standard form
10000000 1 1. calculate the binary form of the number
10000001 2 2. calculate the normalized binary form
10000010 3 3. set the sign bit
10000011 4 4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
… …
11111111 128
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38. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0
Represent 25.010 in IEEE standard
to correspond to
1. 25.010 = 11001.02 we’ll add 127
the table, 1.1001 x 24
2. normalize 11001.02exponent x 24
to the = 1.1001
3. set the sign bit00000000 -127
4. store 4 in the exponent section
00000001 -126
00000010 -125
… …
01111111 0 Steps to represent a number in IEEE standard form
10000000 1 1. calculate the binary form of the number
10000001 2 2. calculate the normalized binary form
10000010 3 3. set the sign bit
10000011 4 4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
… …
11111111 128
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39. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0
Represent 25.010 in IEEE standard
to correspond to
1. 25.010 = 11001.02 we’ll add 127
the table, 1.1001 x 24
2. normalize 11001.02exponent x 24
to the = 1.1001
3. set the sign bit00000000 -127 4 + 127 = 131
4. store 4 in the exponent section
00000001 -126
00000010 -125 131 = 100000112
… …
01111111 0 Steps to represent a number in IEEE standard form
10000000 1 1. calculate the binary form of the number
10000001 2 2. calculate the normalized binary form
10000010 3 3. set the sign bit
10000011 4 4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
… …
11111111 128
MATH1003

40. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 1 1
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 4 + 127 = 131
4. store 4 in the exponent section
131 = 100000112
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

41. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 1 1
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit
4. store 4 in the exponent section
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

42. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 1 1
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 1.1001
4. store 4 in the exponent section
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

43. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
the normalized form
0 1 0 0 0 0 0 1 1 will always have a 1 to the left
of the point, so let’s ignore the 1
Represent 25.010 when we use this number in a
(but
in IEEE standard
1. 25.010 = 11001.02 calculation, we’ll put it “back”) 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 1.1001
4. store 4 in the exponent section
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

44. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
the normalized form
0 1 0 0 0 0 0 1 1 will always have a 1 to the left
of the point, so let’s ignore the 1
Represent 25.010 when we use this number in a
(but
in IEEE standard
1. 25.010 = 11001.02 calculation, we’ll put it “back”) 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 1.1001
4. store 4 in the exponent section
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

45. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 1 1 1 0 0 1
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 1.1001
4. store 4 in the exponent section
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

46. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
we’ll
fill in the rest
with 0s
0 1 0 0 0 0 0 1 1 1 0 0 1
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 1.1001
4. store 4 in the exponent section
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

47. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
we’ll
fill in the rest
with 0s
0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Represent 25.010 in IEEE standard
1. 25.010 = 11001.02 1.1001 x 24
2. normalize 11001.02 = 1.1001 x 24
3. set the sign bit 1.1001
4. store 4 in the exponent section
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

48. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

49. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

50. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

51. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 3410 = 1000102
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

52. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 3410 = 1000102
.2 x 2 = 0.4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

53. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 3410 = 1000102
.2 x 2 = 0.4
.4 x 2 = 0.8
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

54. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 3410 = 1000102
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

55. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 3410 = 1000102
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
.6 x 2 = 1.2
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

56. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 3410 = 1000102
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
.6 x 2 = 1.2
.2 x 2 = 0.4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

57. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 3410 = 1000102
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
.6 x 2 = 1.2
.2 x 2 = 0.4
Steps to represent a number in IEEE standard form
34.210 = 100010.00112
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

58. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

59. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112
2. normalized as 1.000100011 x 25
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

60. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112
2. normalized as 1.000100011 x 25
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

61. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

62. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

63. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
1 1
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

64. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
1 1
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
4. store 5 in the exponent section as (5 + 127 = 132) 100001002
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

65. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
1 1 0 0 0 0 1 0 0 0
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
4. store 5 in the exponent section as (5 + 127 = 132) 100001002
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

66. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
1 1 0 0 0 0 1 0 0 0
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
4. store 5 in the exponent section as (5 + 127 = 132) 100001002
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

67. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
4. store 5 in the exponent section as (5 + 127 = 132) 100001002
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

68. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
we’ll fill in the
Real Numbers rest with the repeating
pattern
1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
4. store 5 in the exponent section as (5 + 127 = 132) 100001002
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

69. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
we’ll fill in the
Real Numbers rest with the repeating
pattern
1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0
Represent -34.210 in IEEE standard
1. 34.210 = 100010.00112 1.000100011 x 25
2. normalized as 1.000100011 x 25
3. set the sign bit
4. store 5 in the exponent section as (5 + 127 = 132) 100001002
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

70. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

71. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

72. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

73. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

74. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

75. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
.1 x 2 = 0.2
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

76. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
.1 x 2 = 0.2
.2 x 2 = 0.4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

77. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
.1 x 2 = 0.2
.2 x 2 = 0.4
.4 x 2 = 0.8
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

78. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
.1 x 2 = 0.2
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

79. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
.1 x 2 = 0.2
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
.6 x 2 = 1.2
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

80. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
.1 x 2 = 0.2
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
.6 x 2 = 1.2
.2 x 2 = 0.4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

81. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 .025 x 2 = 0.05
.05 x 2 = 0.1
.1 x 2 = 0.2
.2 x 2 = 0.4
.4 x 2 = 0.8
.8 x 2 = 1.6
.6 x 2 = 1.2
.2 x 2 = 0.4
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
0.02510 = 0.00000112
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

82. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

83. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 0.000001100110011
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

84. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 0.000001100110011
2. normalized as 1.1001 x 2-6
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

85. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.100110011001
2. normalized as 1.1001 x 2-6
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

86. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.1001 x 2-6
2. normalized as 1.1001 x 2-6
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

87. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.1001 x 2-6
2. normalized as 1.1001 x 2-6
3. set the sign bit
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

88. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 0
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.1001 x 2-6
2. normalized as 1.1001 x 2-6
3. set the sign bit
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

89. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 0
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.1001 x 2-6
2. normalized as 1.1001 x 2-6
3. set the sign bit
4. store -6 in the exponent section as (-6 + 127 = 121) 011110012
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

90. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 0 1 1 1 1 0 0 1 1
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.1001 x 2-6
2. normalized as 1.1001 x 2-6
3. set the sign bit
4. store -6 in the exponent section as (-6 + 127 = 121) 011110012
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

91. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 0 1 1 1 1 0 0 1 1
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.1001 x 2-6
2. normalized as 1.1001 x 2-6
3. set the sign bit
4. store -6 in the exponent section as (-6 + 127 = 121) 011110012
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

92. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0
Represent 0.02510 in IEEE standard
1. 0.02510 = 0.00000112 1.1001 x 2-6
2. normalized as 1.1001 x 2-6
3. set the sign bit
4. store -6 in the exponent section as (-6 + 127 = 121) 011110012
5. store the normalized binary form
Steps to represent a number in IEEE standard form
1. calculate the binary form of the number
2. calculate the normalized binary form
3. set the sign bit
4. store the exponent (+127, store as an 8-bit binary)
5. store the normalized binary form without the first 1
MATH1003

93. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
MATH1003

94. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
MATH1003

95. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10001010 (= 138)
MATH1003

96. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10001010 (= 138)
3. the decimal exponent is 138 - 127 = 11
MATH1003

97. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10001010 (= 138)
3. the decimal exponent is 138 - 127 = 11
4. from the number section, we have 1.112
MATH1003

98. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10001010 (= 138)
3. the decimal exponent is 138 - 127 = 11
4. from the number section, we have 1.112
5. therefore the number is 1.112 x 211
MATH1003

99. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10001010 (= 138)
3. the decimal exponent is 138 - 127 = 11
4. from the number section, we have 1.112
5. therefore the number is 1.112 x 211
6. 1.112 = 1.75 and 211 = 2048
MATH1003

100. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10001010 (= 138)
3. the decimal exponent is 138 - 127 = 11
4. from the number section, we have 1.112
5. therefore the number is 1.112 x 211
6. 1.112 = 1.75 and 211 = 2048
7. 1.75 x 2048 = 3584
MATH1003

101. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10001010 (= 138)
3. the decimal exponent is 138 - 127 = 11
4. from the number section, we have 1.112
5. therefore the number is 1.112 x 211
6. 1.112 = 1.75 and 211 = 2048
7. 1.75 x 2048 = 3584
MATH1003
3584

102. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
MATH1003

103. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
MATH1003

104. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10000000 (= 128)
MATH1003

105. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10000000 (= 128)
3. the decimal exponent is 128 - 127 = 1
MATH1003

106. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Real Numbers
0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Determine the real number
1. since the sign bit is 0, we know this is a positive number
2. the exponent section is 10000000 (= 128)
3. the decimal exponent is 128 - 127 = 1
4. from the number section, we have 1.11001
MATH1003