Hexadecimal ↔ Binary (Fast Direct Conversions - direct nibble mapping)

Hex is the most readable way to look at binary. In this lesson you’ll learn two ways to convert between hexadecimal and binary — including the direct nibble mapping that turns every hex digit into exactly 4 bits (and back) with no arithmetic.

🔹 1️⃣ Hex → Binary: Two Ways

Way 1 (Two-step):

1. Hex → Decimal →
2. Decimal → Binary. (Conceptual but slower).

Way 2 (Direct):
Map each hex digit → 4-bit nibble. (Fastest; what pros use).
Example mapping:

A→1010, B→1011, C→1100, D→1101, E→1110, F→1111. 

Worked examples:

• 1D5₁₆ → 1 | D | 5 → 0001 1101 0101 → 0001 1101 0101.
• 5E9₁₆ → 5 | E | 9 → 0101 1110 1001 → 0101 1110 1001.
• 1DF₁₆ → 1 | D | F → 0001 1101 1111 → 0001 1101 1111.

Tip: Always group the final binary as nibbles (4 bits) for readability. 

🔹 2️⃣ Binary → Hex: Two Ways

Way 1 (Two-step):

1. Binary → Decimal →
2. Decimal → Hex. (Good for theory refresh).

Way 2 (Direct):
Group bits in fours from the right, then map each 4-bit group to one hex digit.

Worked examples :

• 0001 1101 0101₂ → group 0001 | 1101 | 0101 → 1 D 5 → 1D5₁₆.
• 0001 1101 1111₂ → group 0001 | 1101 | 1111 → 1 D F → 1DF₁₆.

🔹 3️⃣ Why Direct Conversion Wins

• Zero arithmetic once you know the nibble table.
• One byte = two hex digits → memory dumps, instruction bytes, and color codes are clean and short.

🔗 Interconnection

• Hex ↔ Binary maps 1 digit ↔ 4 bits (nibble), so 1 byte ↔ 2 hex digits.
  
• Use Way 2 (direct) for speed; use Way 1 to reinforce base-conversion theory.
  
• Grouping in nibbles keeps numbers readable and reduces errors when reading bytes, addresses, and encodings.