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Digital Circuits Assignment 4

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BLG 231E – Digital Circuits
Assignment 4
1. The combinational circuit ARITHMETIC/LOGIC (A/L) performs the following operations
depending on the value of the control inputs X, Y, and Z.
The meanings of symbols are given below:
X Y Z Result (O) Cout
0 0 0 B – A Borrow
0 0 1 A + B Carry
0 1 0 A – 5 Borrow
0 1 1 Φ Φ
1 0 0 A ⋅ B Φ
1 0 1 Φ Φ
1 1 0 A ⊕ B Φ
1 1 1 Φ Φ
Symbol Meaning
+ Arithmetic addition
– Arithmetic subtraction
⋅ 4-bit logic AND between corresponding bits of A and B: A3⋅B3, …, A0⋅B0.
⊕ 4-bit logic XOR between corresponding bits of A and B: A3⊕B3, …, A0⊕B0.
Φ Don’t care
Page 2 of 2
Design and draw this circuit using only the standard components and logic gates given below,
paying attention to the maximum number allowed for the first three:
Note: Even though we have not specified a maximum number allowed on the last four, you
should try to use as few as possible (also, you do not need to use all of the gates listed above).
Your design should be as simple as possible, containing the fewest number of standard
components and logic gates.
Type Maximum number allowed
4-bit parallel adders 2
8:1 multiplexer 1
2:4 decoder 1
XOR gates No restriction
NOT gates No restriction
OR gates No restriction
AND gates No restriction

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