BCD Code (8421) — Binary Coded Decimal Complete Guide

What is BCD?

BCD (Binary Coded Decimal) is a class of binary encoding where each decimal digit (0–9) is represented independently using a 4-bit binary code.

The name "8421" comes from the positional weights: 8, 4, 2, 1 (standard binary weights for 4 bits).

Key rule: Only the combinations 0000 to 1001 are valid BCD digits. Codes 1010 through 1111 are invalid/forbidden in BCD.

Converting BCD to Decimal

Group bits in sets of 4 from right; convert each group to decimal.

Example: Convert 0110 1000 0101 to Decimal

BCD vs Pure Binary

BCD Addition

Add the two 4-bit BCD digits as binary. If the sum exceeds 9 (i.e., > 1001) or produces a carry, add 6 (0110) to correct.

Rule

Example 1: Add BCD 5 + 3

Example 2: Add BCD 7 + 8

Example 3: Add BCD 37 + 48

Numerical Examples (GATE Level)

Q1: Convert decimal 396 to BCD.

Q2: What is 0111 1000 in BCD decimal?

Q3: Add BCD 59 + 47.

Advantages of BCD

1. Easy conversion to/from decimal (used in calculators, displays)
2. No conversion needed to drive 7-segment displays
3. Avoids rounding errors in financial calculations

Disadvantages of BCD

1. Less storage-efficient than pure binary (wastes 6 codes per digit)
2. Arithmetic requires correction step
3. Slower arithmetic circuits

Interview Questions

Q1: Why are codes 1010–1111 invalid in BCD? BCD maps each decimal digit (0–9) to a 4-bit code. Since decimal has only 10 digits, only 10 of the 16 possible 4-bit combinations are used. The remaining 6 combinations (1010–1111) have no decimal equivalent and are treated as invalid.

Q2: How many BCD digits are needed to represent decimal 999? Three BCD digits × 4 bits each = 12 bits. Pure binary only needs 10 bits (2^10 = 1024). BCD uses 20% more bits here.

Q3: What correction factor is added in BCD addition and why 6? When a sum exceeds 9, adding 6 (= 16 - 10) corrects for the fact that BCD skips 6 codes between 9 (1001) and the next decimal digit carry (10000). Adding 6 effectively performs the decimal carry correction.

Q4: Where is BCD practically used today? BCD is used in digital clocks/watches (seconds, minutes display), financial calculations (banking software to avoid floating-point errors), 7-segment display decoders (7447 IC), and ATM machines.

Q5: What is the difference between BCD and binary? Binary is a pure number system — 8 bits can represent 0–255. BCD is a coded representation — 8 bits represent only 0–99 (two decimal digits). BCD prioritizes decimal readability over storage efficiency.