Below is a step-by-step tutorial showing how to convert a binary number into Decimal, Octal, and Hexadecimal Number system.

Example Binary Number

Let’s use:

Binary = 101101.101₂

This number has:

• Integer part → 101101
• Fraction part → .101

1) Binary ➜ Decimal Conversion

Rule

Each binary digit represents a power of 2.

Positions left of decimal:
… 2⁵ 2⁴ 2³ 2² 2¹ 2⁰

Positions right of decimal:
2⁻¹ 2⁻² 2⁻³ …

Step 1: Convert Integer Part (101101₂)

Write powers of 2 under each digit:

Now multiply and add:

= 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×1
= 32 + 0 + 8 + 4 + 0 + 1
= 45

Step 2: Convert Fraction Part (.101₂)

= 1×½ + 0×¼ + 1×⅛
= 0.5 + 0 + 0.125
= 0.625

Final Decimal Answer

101101.101₂ = 45.625₁₀

2) Binary ➜ Octal Conversion

Rule

Group binary digits in sets of 3 bits from the decimal point.

Step 1: Group Integer Part

Binary: 101101
Group into 3 bits from right:

101 101

Convert each group to decimal:

Integer part → 55₈

Step 2: Group Fraction Part

Fraction: .101
Group from left:

101

Fraction part → .5₈

Final Octal Answer

101101.101₂ = 55.5₈

3) Binary ➜ Hexadecimal Conversion

Rule

Group binary digits in sets of 4 bits.

Step 1: Group Integer Part

Binary: 101101
Add leading zeros to make groups of 4:

0010 1101

Convert each group:

Integer part → 2D

Step 2: Group Fraction Part

Fraction: .101
Add trailing zeros:

.1010

Fraction part → .A

Final Hexadecimal Answer

101101.101₂ = 2D.A₁₆

Final Summary Table