Design Problem You need to use a magnitude comparator for a circuit you are building. You would like to compare two 4-bit signed numbers, X = ABCD and Y = EFGH, whose possible values range from -31o to 310. However, it seems that all magnitude comparators are out of stock. Suppose you decide to recreate the behavior of a magnitude comparator using your 4-bit full adder as a subtractor and some logic gates on hand. Use a 4-bit adder and connect additional logic gates to the input and the 4-bit output Sum (S3S2S1 So) to create the logic circuit for the following outputs: • 01, which should be 1 if X < Y or X = Y,0 otherwise • O2, which should be 1 if X > Y or X = Y,0 otherwise a) Make truth table for the outputs 01 and Ozusing the 4-bit output Sum (S3S2S1So) as inputs b) Derive an equation for O1. c) Derive an equation for O2.
Design Problem You need to use a magnitude comparator for a circuit you are building. You would like to compare two 4-bit signed numbers, X = ABCD and Y = EFGH, whose possible values range from -31o to 310. However, it seems that all magnitude comparators are out of stock. Suppose you decide to recreate the behavior of a magnitude comparator using your 4-bit full adder as a subtractor and some logic gates on hand. Use a 4-bit adder and connect additional logic gates to the input and the 4-bit output Sum (S3S2S1 So) to create the logic circuit for the following outputs: • 01, which should be 1 if X < Y or X = Y,0 otherwise • O2, which should be 1 if X > Y or X = Y,0 otherwise a) Make truth table for the outputs 01 and Ozusing the 4-bit output Sum (S3S2S1So) as inputs b) Derive an equation for O1. c) Derive an equation for O2.
Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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Transcribed Image Text:Design Problem
You need to use a magnitude comparator for a circuit you are building. You would like to compare two 4-bit signed numbers, X = ABCD and Y = EFGH, whose possible values
range from –310 to 310. However, it seems that all magnitude comparators are out of stock. Suppose you decide to recreate the behavior of a magnitude comparator using your 4-bit
full adder as a subtractor and some logic gates on hand.
Use a 4-bit adder and connect additional logic gates to the input and the 4-bit output Sum (S3 S2 S1 So) to create the logic circuit for the following outputs:
• 01, which should be 1 if X <Y or X = Y,0 otherwise
• 02, which should be 1 if X > Y or X = Y,0 otherwise
a) Make truth table for the outputs 01 and Ozusing the 4-bit output
Sum (S3S2S1S0) as inputs
b) Derive an equation for O.
c) Derive an equation for O2.
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