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Digital Circuits Assignment 1

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BLG 231E – Digital Circuits
Assignment 1
Part 1 – Computer Arithmetic
1. A and B are two 8-bit binary integers, and B = 1101 1001. For the operation A – B, answer the following
questions:
a. If A and B are signed binary integers, what are the i) largest and ii) smallest decimal values of A that
yield valid results (that can be represented using 8 bits) after the operation? Explain your answer
briefly.
b. Write the binary representation for the largest value of the signed A you found in (a.i). Carry out the
binary operation A – B using 2’s complement, and show that the result is valid using binary numbers
only.
c. If A and B are unsigned binary integers, what are the i) largest and ii) smallest binary values of A
that yield valid results after the operation? Explain your answer briefly.
2. A and B are two 8-bit, signed, binary integers, and A = 1011 1100. If we perform the operation A + B ,
a. What are the i) largest and ii) smallest decimal values of B that yield valid results after the operation?
Explain your answer briefly.
b. Write the binary representation for the smallest value of the signed B you found in (a.ii). Perform
the binary operation A + B, and show that the result is valid using binary numbers only.
Part 2 – Boolean Algebra
3. Simplify the following logic expressions using axioms, properties, and theorems of Boolean algebra.
a. 𝐸(𝑎, 𝑏, 𝑐) = 𝑎𝑏̅𝑐 + 𝑎𝑏𝑐̅+ 𝑎𝑏𝑐 + 𝑎̅𝑏𝑐
b. 𝐸(𝑎, 𝑏, 𝑐, 𝑑) = 𝑎̅𝑏𝑑̅+ 𝑏𝑐𝑑 + 𝑎𝑏𝑐̅+ 𝑎𝑏̅𝑑 + 𝑏𝑐̅𝑑̅+ 𝑎𝑑 + 𝑎̅𝑏𝑐

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