Question 4# Read the following algorithm: Algorithm for converting a fraction a into binary with p binary places. Inputs: fraction z EQ, 0

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Question 4# Read the following algorithm:
Algorithm for converting a fraction into binary with p binary places.
Inputs: fraction r EQ, 0<x< 1 and number of places p E N.
Outputs: bits b₁,b2,..., bp such that (0.bybą... bp)2 is the
best approximation to z using p binary places.
Method:
Initialise: j1, b₁,b2,...,bp0
Loop: if j = p + 1 stop.
x + 2x
If r≥1 [b, 1, x-x-1]
j+j+1
Repeat loop
(a) Verify that the algorithm converts to 0.11010, when p=5. Can you spot how to
express exactly in repeating binary?
(b) Express 0.8510 as accurately as possible with 8 binary places.
Transcribed Image Text:Question 4# Read the following algorithm: Algorithm for converting a fraction into binary with p binary places. Inputs: fraction r EQ, 0<x< 1 and number of places p E N. Outputs: bits b₁,b2,..., bp such that (0.bybą... bp)2 is the best approximation to z using p binary places. Method: Initialise: j1, b₁,b2,...,bp0 Loop: if j = p + 1 stop. x + 2x If r≥1 [b, 1, x-x-1] j+j+1 Repeat loop (a) Verify that the algorithm converts to 0.11010, when p=5. Can you spot how to express exactly in repeating binary? (b) Express 0.8510 as accurately as possible with 8 binary places.
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