This image shows the internal design of a 4-bit ___________, this type of compon

Question

This image shows the internal design of a 4-bit ___________, this type of component is also known as ___________.

In a scenario where each logic gate has a delay of 5 nanoseconds, and all wires connecting them are assumed to have no delay, this component has a delay of __________ nanosecond(s).

a3 b3 a2 b2 a1b a0 b0 eq This design which uses XNOR gates is very scalable because the number of gates it requires grows linearly, to compare two 8-bit numbers we need XNOR gates. XNOR gates, and to compare two 16-bit numbers we need In a different approach, if a component with the similar function were to be designed using the combinational logic design process, the simplified truth table that enumerates all the possible situations for which all the bits are equal (since only those situations would have a 1 in the column for the output eq) would grow exponentially with respect to the number of bits of the numbers being compared; for instance, to compare two 8-bit numbers that simplified table would have rows (entries), and to compare two 16-bit numbers that simplified table would have rows (entries) Note: Be aware that the last text boxes refer to numbers of rows not in the full table, but in a simplified truth table in which both numbers being compared are equal (hence the output eq is always 1).

Explanation / Answer

The above image shows N-bit equality comparator: Outputs 1 if two N-bit numbers are equal
– 4-bit equality comparator with inputs A and B
• a3 must equal b3, a2 = b2, a1 = b1, a0 = b0
– Two bits are equal if both 1, or both 0
– eq = (a3b3 + a3’b3’) * (a2b2 + a2’b2’) * (a1b1 + a1’b1’) * (a0b0 + a0’b0’)
• Recall that XNOR outputs 1 if its two input bits are the same
– eq = (a3 xnor b3) * (a2 xnor b2) * (a1 xnor b1) * (a0 xnor b0)

delay: if each gate has a delay of 1 ns then each stage will have a delay of 2 gate-delays. So for a 4 bit magnitude comparator delay is (4 stages)*(2 gate-dalays/stage)= 8 gate-delays.

To compare two 8 bit numbers we need 8 XNOR gates.

To compare two 16 bit numbers we need 16 XNOR gates.

I think to compare two 8 bit numbers we need 13 row entrie s in truth table and 16 row entries.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.