Download presentation

Presentation is loading. Please wait.

Published byEdwin Cumming Modified over 4 years ago

1
Fixed-point and floating-point numbers CS370 Fall 2003

2
2 Representations of numbers Unsigned integers Signed integers – 1’s and 2’s complement representation To represent –Very Large and very Small numbers –Real numbers in general Fixed-point numbers Floating-point numbers

3
3 Base-10 (decimal) arithmetic Uses the ten numbers from 0 to 9 Each column represents a power of 10

4
4 Base-10 (decimal) arithmetic Uses the ten numbers from 0 to 9 Each column represents a power of 10

5
5 Standard binary representation Uses the two numbers from 0 to 1 Every column represents a power of 2

6
6 Fixed-point representation Uses the two numbers from 0 to 1 Every column represents a power of 2

7
7 Addition Base-10Base-2

8
8 Range of values in a byte

9
9 Scientific notation (1) One billion =1,000,000,000 =1 x 10 9 –significand or mantissa: 1 –base or radix: 10 –exponent: 9

10
10 Scientific notation (2) 1999 =1.999 x 10 3 –significand or mantissa: 1999 –base or radix: 10 –exponent: 3 =19.99 x 10 =199.9 x 10

11
11 Practice (base 10) 258 = 2.58 x 10 2 Mantissa = 258 Radix = 10 Exponent = 2 24.25 = 2.425 x 10 1 Mantissa = 2425 Radix = 10 Exponent = 1

12
12 Base-2 scientific notation 2.25 ten =10.01 two =10.01 two x 2 0 =1.001 two x 2 1 normalized Numbers are usually normalized which means that the leading bit is always a 1.

13
13 8-bit floating point format (1) sign 1 bit exponent 3 bits significand 4 bits number base 2 number base 10 000110011.001x2 1 2.25 001111001.1 x 2 3 12.0 011111101.11 x 2 7 224.0 100111101.11 x 2 -1 0.875

14
14 Improvements Bias the exponent –Always subtract a fixed amount, e.g., 3 –Allows representation of negative exponents Implicit one -Leading one in a Phone number such as 1-619-556-0231 is redundant. –Why use a bit for the leading one?

15
15 8-bit floating-point format (2) Exponent (3 bits) is biased by 3 The leading one of significand is implicit Zero is represented by all zeros

16
16 IEEE standard floating-point Single precision –32 bits sign: 1 bit exponent: 8 bits significand: 23 bits –Bias: 127 Double precision –64 bits sign: 1 bit exponent: 11 bits significand: 52 bits –Bias: 511

17
17 Practice( base 10) 13 = 1.3 x 10 1 = 1.011 x 2 3 1.25 = 1.25 x 10 0 = 1.010 x 2 0

18
18

19
19

Similar presentations

Presentation is loading. Please wait....

OK

Floating Point Numbers

Floating Point Numbers

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google