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Radix Point Shift Calculator

Shift radix point left/right in any base with detailed step-by-step derivation

Input Number
Base
Shift Amount
Shift Direction

Radix Point Shift Principle

① Shift left n positions: Multiply by base^n
② Shift right n positions: Divide by base^n
③ Beyond digits: Pad with zeros as placeholders

Radix point shifting is a fundamental operation in floating-point arithmetic and scientific notation across all number bases.

Positive shifts left (multiply), negative shifts right (divide). Zeros are automatically added as needed for padding.

What Is Radix Point Shifting?

The radix point (decimal point in base 10) separates the integer and fractional parts. Shifting it changes the magnitude by powers of the base.

Left Shift = Multiply

Shift left by n = multiply by base^n. Decimal 123.45 shifted left by 1 = 1234.5 (×10).

Right Shift = Divide

Shift right by n = divide by base^n. Decimal 123.45 shifted right by 1 = 12.345 (÷10).

Zero Padding

When shifting beyond digits, add zeros. Binary 101 left shifted by 2 = 10100 (two zeros).

Floating-Point

Radix point shifting is essential for floating-point normalization, scientific notation, and efficient arithmetic.

💡 Teaching Example: Binary 1101.101 shifted left by 2. Move radix point 2 right → 110110.1. This is equivalent to multiplying by 2² = 4.

Applications

Floating-Point Scientific Notation Computer Arithmetic Normalization Education

Frequently Asked Questions

What is a radix point shift?
A radix point shift moves the decimal point (or radix point) left or right. Shifting right divides by the base; shifting left multiplies by the base. For example, in decimal, 123.45 shifted right by 1 = 12.345 (divided by 10).
How does radix point shifting relate to multiplication/division?
Shifting left by n positions is equivalent to multiplying by base^n. Shifting right by n positions is equivalent to dividing by base^n. This is why it's fundamental in floating-point arithmetic!
Why is radix point shifting important in computing?
Radix point shifting is core to floating-point number representation (IEEE 754), scientific notation, normalization, and efficient arithmetic operations in computers.
What happens when you shift beyond digits?
When shifting beyond available digits, zeros are added as placeholders. For example, binary 101 shifted left by 2 = 10100 (two zeros added on the right).

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