1. Construct a table all possible m=4 bit sequences. Assuming 1 bit is 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.
1. Construct a table all possible m=4 bit sequences. Assuming 1 bit is 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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8bd1e73-ae88-4a23-a327-a46419b3c04f%2Fbcb49613-3160-4d0a-8e23-a6e1b4c2f80f%2F6q7kzf_processed.jpeg&w=3840&q=75)
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.
![1. Construct a table all possible m=4 bit sequences.
Assuming 1 bit is 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8bd1e73-ae88-4a23-a327-a46419b3c04f%2Fbcb49613-3160-4d0a-8e23-a6e1b4c2f80f%2Fju6arqb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Construct a table all possible m=4 bit sequences.
Assuming 1 bit is 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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