Binary Coded Decimal (BCD): Insifix
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Posted by Gautam Kumar | Last Updated: 03 Feb, 2026

Binary Coded Decimal (BCD) is a system where each decimal digit (0-9) is represented by a fixed 4-bit binary sequence. Unlike standard binary numbers, BCD handles each digit separately.

Key Features

  • Decimal-Oriented: Represents numbers digit-by-digit rather than as a whole value.
  • Display Ready: Used in digital clocks and calculators for easy output to screens.
  • Precision: Allows for accurate decimal arithmetic, avoiding rounding errors.

Visualizing BCD Conversion

57 Decimal 0101 (Digit 5) 0111 (Digit 7) = 0101 0111 BCD Representation

How BCD Works

In BCD, every decimal digit is converted into a 4-bit binary code.

Truth Table

DecimalBCD Code
00000
10001
20010
30011
40100
50101
60110
70111
81000
91001

BCD Storage Types

1. Packed BCD

Stores two decimal digits in one byte (8 bits).

  • Format: 4 bits for the first digit, 4 bits for the second.
  • Example (93): 1001 (9) + 0011 (3) = 10010011

2. Unpacked BCD

Stores one decimal digit per byte (8 bits).

  • Example (93): 00001001 (9) and 00000011 (3).

Arithmetic Operations

1. BCD Addition

Add the binary codes. If a 4-bit sum exceeds 9 (1001), add 6 (0110) to correct it.

   0100 0101  (45)
+  0011 0111  (37)
------------
   0111 1100  (Sum is 12, which is > 9)
+  0000 0110  (Add 6 to correct)
------------
   1000 0010  (Result: 82)

2. BCD Subtraction

Subtraction is often performed by adding the complement, or by simple binary subtraction with correction. If a borrow occurs from the next group, 6 is subtracted.

      0100 0111  (47)
   -  0010 0011  (23)
   ------------
      0010 0100  (Result: 24 - No correction needed)

3. BCD Multiplication

Multiplication is usually done by converting BCD to binary, multiplying, and converting back to BCD.

    5 x 3 = 15
    Binary: 0101 (5) x 0011 (3) = 0000 1111 (15)
    Convert 15 to BCD:
    1 -> 0001
    5 -> 0101
    Result: 0001 0101

4. BCD Division

Similar to multiplication, division is best handled by converting to binary first.

    18 / 3 = 6
    Binary: 10010 (18) / 0011 (3) = 0110 (6)
    Convert 6 to BCD: 0110

Quick Quiz

1. BCD is primarily used in:
A) Digital displays ✅
B) RAM storage

2. The BCD code for decimal 5 is:
A) 0110
B) 0101 ✅

3. The correction factor for BCD addition is:
A) 3
B) 6 ✅

Frequently Asked Questions (FAQ)

What is binary coded decimal (BCD)? BCD is a numerical scheme where each decimal digit is encoded individually using four binary bits. It acts as a bridge between human decimal numbers and computer binary systems.
What is the advantage of using BCD? Its main advantage is precision. It eliminates the rounding errors common in floating-point binary math, making it essential for financial calculations and timekeeping.
What is the difference between BCD and binary? Binary represents a number as a single sequence of bits. BCD represents each decimal digit separately (digit-by-digit). Binary is more compact; BCD is more precise for decimal fractions.
What is the maximum value that can be represented in BCD? A single BCD digit (4 bits) can represent 9. Two BCD digits (8 bits) can represent 99.
What are some common applications of BCD? It is used in calculators, digital clocks, petrol pumps, cash registers, and accounting systems.
How is BCD used in programming? It is often used via software libraries for arbitrary-precision arithmetic (like `Decimal` in Python) to ensure financial accuracy.
What is BCD code conversion? It is the process of converting a number from standard binary or decimal into BCD format, usually for output to a display.
What is the difference between unpacked BCD and packed BCD? Packed BCD stores two digits per byte (efficient). Unpacked BCD stores one digit per byte (easier to process but wastes space).
How is BCD used in digital clocks? Real-time clock circuits count seconds, minutes, and hours directly in BCD format to easily drive 7-segment displays without complex conversion logic.
What is the difference between BCD and ASCII? BCD is for numbers (math/display). ASCII is for text. For example, '9' in BCD is `1001` (4 bits), but in ASCII it is `00111001` (8 bits).
How is BCD used in data storage? It allows for storing exact decimal values in a compact nibble format, which is useful for databases storing currency.
What is the difference between BCD and Gray code? BCD is a weighted code for arithmetic (8-4-2-1). Gray code is unweighted and designed so that only one bit changes at a time to prevent hardware errors.
What is the purpose of BCD correction? Since 4 bits can hold 16 values (0-15) but BCD only uses 10 (0-9), we add 6 to skip the invalid states when a sum exceeds 9.
What is the difference between BCD and excess-3 code? Excess-3 is BCD plus 3 (e.g., 0 is `0011`). It is self-complementing, which helps in subtraction circuits. BCD is a direct translation of the digit.
What is the advantage of using BCD in financial calculations? It ensures that values like $0.10 are stored exactly, whereas standard binary often stores them as approximating repeating fractions (0.000110011...).
How does BCD arithmetic differ from binary arithmetic? BCD arithmetic operates digit-by-digit and checks for invalid codes (greater than 9) after every step. Binary arithmetic operates on the whole number at once.
What is the purpose of BCD-to-7-segment conversion? This process takes the 4-bit BCD code and activates the specific LED segments (a-g) needed to visually display that number.
What is the purpose of BCD adders? BCD adders are specialized hardware circuits that automatically detect sums over 9 and add the correction factor (6) in real-time.
How does BCD differ from Gray code in terms of bit patterns? BCD patterns are sequential numbers (0000, 0001...). Gray code patterns are arranged to minimize bit switching (0000, 0001, 0011...).
What is the difference between BCD and excess-127 code? Excess-127 is used for exponents in floating-point binary (IEEE 754). BCD is used for the mantissa (the actual digits) in decimal arithmetic.
How does BCD differ from ASCII code in terms of data transmission? BCD is more bandwidth-efficient for numbers (4 bits/digit) compared to ASCII (8 bits/character).
What is the purpose of BCD-to-decimal conversion? To convert machine-stored BCD data back into a standard integer format for calculation or processing by standard binary CPUs.
What is the purpose of BCD-to-ASCII conversion? To convert numerical data into a text string format suitable for printing, logging files, or displaying on a computer monitor.