IEEE Transactions on Circuits and Systems—I: Regular Papers

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What are the three main computation stages of multipliers?

Partial Product (PP) generation, PP accumulation (reduction), final addition

Name three main architectures used to accumulate Partial Products (PPs) in multipliers.

Carry-Save Adder (CSA) array, Wallace tree, Dadda tree

What is one advantage of tree-based PP accumulation over array structures?

Less delay

What is one advantage of array-based multipliers over tree-based architectures?

Simple, uniform, and modular architecture Signup and view all the answers

How do designers employ approximation in multipliers?

By using operand truncation and approximation during PP accumulation stage Signup and view all the answers

What is one way to reduce the complexity of a multiplier through approximation?

Operand truncation Signup and view all the answers

What is one of the emerging computing paradigms discussed in the text?

Approximate computing Signup and view all the answers

How do approximate computations impact calculation complexities?

Reduce significantly Signup and view all the answers

What is the proposed methodology for designing approximate N-bit array multipliers based on?

Carry disregarding Signup and view all the answers

What percentage reduction in critical path delay is achieved by the proposed 8-bit multipliers compared to the exact multiplier?

29% Signup and view all the answers

How do the proposed 16-bit multipliers perform in terms of power consumption compared to the exact 16-bit multiplier?

Reduced by 24% on average Signup and view all the answers

What improvement is achieved by the proposed 16-bit multipliers in terms of area compared to the exact 16-bit multiplier?

23% on average Signup and view all the answers

What is the primary purpose of using approximate computing in the calculations of an 8-bit multiplier?

To reduce the dependence between 50s and achieve a better balance between accuracy and critical path delay, power consumption, and area. Signup and view all the answers

How does a CLA (Carry Look-Ahead) structure impact the delay in calculating the sum of the results of two 8 × 4 multipliers?

Significantly reduces the delay due to carries propagation. Signup and view all the answers

What is the leading reason for the strong dependence between 50s in the 8-bit multiplier?

Carry propagation in 50s of 8×4 multipliers. Signup and view all the answers

How does operating 8 × 4 multipliers in parallel impact the 8-bit multiplier delay?

Significantly reduces the 8-bit multiplier delay. Signup and view all the answers

What is the key advantage of disregarding carries in 50 columns of the 8-bit multiplier?

Each column can operate in parallel independently, reducing delay. Signup and view all the answers

How does the proposed approximate 8-bit multipliers architecture aim to improve performance?

By reducing the critical path delay in 8×4 multipliers. Signup and view all the answers

What performance metrics are used to measure the impact of approximating more partial product units in Gaussian smoothing?

Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) Signup and view all the answers

What is the baseline for comparing the performance of the proposed 8-bit approximate multipliers?

Output image of the exact 8-bit multiplier with exact partial product units (50) in Group A and Group B Signup and view all the answers

What type of filter is used for image smoothing in the experimental setup?

Two-dimensional rotationally symmetric 3 × 3 Gaussian low-pass filter Signup and view all the answers

How are the kernel values adjusted to be appropriate for the 8-bit input multipliers?

The kernel's floating-point values are rounded after being multiplied by 210 Signup and view all the answers

What specific type of filter is applied to blur the test image in the study?

Gaussian smoothing filter Signup and view all the answers

What mathematical operation is involved in preparing the initial and revised kernels for the Gaussian low-pass filter?

Multiplication Signup and view all the answers

What is the equation for calculating E Dcd y for the inputs Ai and Bi?

E Dcd y (Ai , Bi ) = E Dx8y (Ai , Bi ) = \sum_{k=0}^{y} x X 2k \times Ck∗ (Ai , Bi ) Signup and view all the answers

How is the error distance E Di calculated for any design of CDM16?

E D 16 = E D 8X 1Y 1 + 28 (E D 8X 2Y 2 ) + 28 (E D 8X 3Y 3 ) Signup and view all the answers

What does the equation Rm 1 = A L B L - E D 8X 1Y 1 (A L , B L ) represent?

It represents the first multiplier unit MU L_1's error calculation using Equation (8). Signup and view all the answers

How is the error distance E D 16 distributed among different components?

The error distance E D 16 is distributed among the four CDM8s and the four CLAxs. Signup and view all the answers

What is the general formula for Rm 2, Rm 3, and Rm 4 in terms of error distances?

Rm 2 = Rm 3 = Rm 4 = Rm i = Rm i _H = + 216 (E D 8X 4Y 4 ) + 28 (E DC L Ax_L ) + 216 (E DC L Ax_M ) Signup and view all the answers

How is the E Di equation for any design of CDM16 generalized for CDM(N - bit) multipliers?

The E Di equation for any design of CDM16 is generalized by considering the E Di of the four CDM8s and the four CLAxs. Signup and view all the answers

IEEE Transactions on Circuits and Systems—I: Regular Papers - Approximate Multipliers

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