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Arithmetic Shift Calculator

Compute arithmetic right shifts with sign-bit preservation (replicated MSB) for signed integers. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Signed Value (Decimal or Binary)

Enter a signed number.

Shift Amount

Calculated Output

Primary Representation

Calculating...

Step-by-Step Mathematical Proof

Active Derivation

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Concept

What Is Arithmetic Shift Calculator?

An Arithmetic Shift is a bit shift designed for signed Two’s Complement integers. Arithmetic Shift Right (ASR / SRA) preserves the sign of negative numbers by replicating the most significant bit (sign extension) into the vacant positions on the left.

Methodology

How Does It Work?

During Arithmetic Right Shift, if the MSB is 1 (negative), 1s are shifted in from the left; if the MSB is 0 (positive), 0s are shifted in. This guarantees that negative numbers remain negative.

Formula & Rules

Mathematical Algorithm

\text{ASR}(X, k): \quad \text{MSB}_i = \text{MSB}_{\text{original}} \quad \text{for inserted bits}

Worked Problem

Step-by-Step Example

Arithmetic right shift -16 >> 2 (8-bit register): -16 in 8-bit Two’s Complement: 11110000 Shift right by 2 with sign bit (1) replication: 11111100 11111100_2 represents -4 (which is -16 / 4).

Important Rules & Edge Cases

The sign bit (MSB) is copied into all newly opened positions on the left.
Preserves the sign of negative integers during division by 2^k.

Practical Applications in Engineering

Signed integer division in CPU compilers without division instructions.
Audio processing volume scaling on signed PCM waveform samples.
Fixed-point signed math in embedded DSPs.

Common Mistakes to Avoid

Caution: Inserting zeros on negative numbers (which turns negative numbers into positive numbers).
Caution: Forgetting that arithmetic right shift floors toward negative infinity (-1 >> 1 = -1).

FAQ