2. Construct a table similar to the one above with m=5 bits. Assuming 3 bits are used for representing the fractional part, convert each binary sequence to its decimal equivalent. a. What is the smallest increment between any two decimal numbers on the list? b. Consider any number 'z' on your list and find the binary sequence for '2z'. Verify the left and right shift properties discussed above

Systems Architecture
7th Edition
ISBN:9781305080195
Author:Stephen D. Burd
Publisher:Stephen D. Burd
Chapter8: Data And Network Communication Technology
Section: Chapter Questions
Problem 31VE
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Example: Assuming m-7 bits and using three of those bits for
representing the fractional part,
( 1100.000 )2
( 0110.000 )2
( 0011.000 )2
( 0001.100 )2
( 0000.110 )2
( 0000.011 )2
(12)10
%3D
(12)10 / 2
(6)10
(6)10 /2
(3)10
(3)10 /2
(1.5)10
(1.5)10 / 2 (0.75)10
(0.75)10 / 2 (0.375)10
In this case, each successive division by two has shifted the
binary sequence to the right by one bit.
Transcribed Image Text:Example: Assuming m-7 bits and using three of those bits for representing the fractional part, ( 1100.000 )2 ( 0110.000 )2 ( 0011.000 )2 ( 0001.100 )2 ( 0000.110 )2 ( 0000.011 )2 (12)10 %3D (12)10 / 2 (6)10 (6)10 /2 (3)10 (3)10 /2 (1.5)10 (1.5)10 / 2 (0.75)10 (0.75)10 / 2 (0.375)10 In this case, each successive division by two has shifted the binary sequence to the right by one bit.
2. Construct a table similar to the one above with m=5 bits.
Assuming 3 bits are used for representing the fractional
part, convert each binary sequence to its decimal
equivalent.
a. What is the smallest increment between any two
decimal numbers on the list?
b. Consider any number 'z' on your list and find the
binary sequence for '2z'. Verify the left and right
shift properties discussed above.
Transcribed Image Text:2. Construct a table similar to the one above with m=5 bits. Assuming 3 bits are used for representing the fractional part, convert each binary sequence to its decimal equivalent. a. What is the smallest increment between any two decimal numbers on the list? b. Consider any number 'z' on your list and find the binary sequence for '2z'. Verify the left and right shift properties discussed above.
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