Types of Adders: Carry Look-Ahead, Carry Save, Carry Select, Carry Skip, Carry Increment

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Questions and Answers

What is the total propagation delay of a 4-bit carry look ahead adder?

40ns
50ns
60ns (correct)
30ns

Which gate in the 4-bit carry look ahead adder has a propagation delay of 20ns?

External Ex-OR gate (correct)
Internal AND gate
Next level OR gate
None of the above

What is the function of an AND gate in a full adder circuit?

Generates the carry output (correct)
Calculates the sum output
Performs exclusive OR operation
None of the above

When is a carry look ahead adder most suitable to use?

High-speed applications (D) Signup and view all the answers

Why would one choose a parallel adder over a carry look ahead adder?

For low-power adders in low-speed applications (A) Signup and view all the answers

What is the total propagation time in a circuit equal to?

The propagation delay of a typical gate multiplied by the number of gate levels (B) Signup and view all the answers

When will the value of Si in an adder be in its steady-state final value?

After the input carry has been propagated (B) Signup and view all the answers

What is the worst-case delay equation for a n-bit carry-ripple adder?

$n$ (D) Signup and view all the answers

How is the worst-case delay calculated for a 16-bit ripple carry adder?

$15 \text{ ns} + (15 \times 12 \text{ ns})$ (D) Signup and view all the answers

Why is the time consumed during the addition process critical for arithmetic operations?

To ensure efficiency in computation (C) Signup and view all the answers

What is a technique for reducing carry propagation time in a parallel adder?

Utilizing carry-lookahead adders (B) Signup and view all the answers

What is the most widely used technique for fast addition in computers?

Carry Look Ahead Adder (D) Signup and view all the answers

How many AND gates and OR gates are required for a n-bit carry lookahead adder to evaluate all the carry bits?

$\frac{n(n + 1)}{2}$ AND gates and $n$ OR gates (D) Signup and view all the answers

What settles to their steady-state values after propagating through their respective gates in half adders?

Pi and Gi signals (D) Signup and view all the answers

How does the Carry Look Ahead Adder achieve a gain in speed of operation?

By propagating C3 simultaneously with C1 and C2 (B) Signup and view all the answers

What is the trade-off associated with the speed gain achieved by Carry Look Ahead Adder?

Higher power consumption (C) Signup and view all the answers

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Study Notes

Carry Look-Ahead Adder

Uses the principle of carry lookahead logic
Requires [n(n + 1)]/2 AND gates and n OR gates for an n-bit adder
Can add in less time because C3 does not have to wait for C2 and C1 to propagate
Gain in speed of operation achieved at the expense of additional complexity (hardware)

Performance of 4-Bit Carry Look Ahead Adder

Propagation delay of Ex-OR gate: 20ns
Propagation delay of AND and OR gates: 10ns
Total propagation delay: 60ns (20ns + 10ns + 10ns + 20ns)

Comparison of Adders

Carry Look Ahead Adder:
- Fast
- Complex
- Large
- High power consumption
- Suitable for high-speed applications
Parallel Adder:
- Slow
- Simple
- Small
- Low power consumption
- Suitable for low-speed applications

Propagation Delay

Total propagation time equals the propagation delay of a typical gate times the number of gate levels in the circuit
Value of Si at any given stage in the adder will be in its steady-state final value only after the input carry to that stage has been propagated

Ripple Carry Adder

General equation for worst-case delay for n-bit carry-ripple adder: not specified
Example: 16-bit ripple carry adder using 16 identical full adders
- Carry propagation delay of each full adder: 12 ns
- Sum propagation delay of each full adder: 15 ns
- Worst-case delay: 195 ns