Binary Coded Decimal (BCD)

4 minAS Level1.1.21.1.4

By the end of this lesson

By the end you can write a denary number in BCD, read BCD back, and explain where and why BCD is used.

Definition

A representation in which each denary digit is stored separately as its own 4-bit binary code (a nibble), from 0000 for 0 to 1001 for 9.

One digit, one nibble

Pure binary converts the whole value at once. BCD refuses to: it takes the denary digits one at a time.

Only 10 of the 16 possible nibbles are used: 0000 to 1001.
The six codes 1010 to 1111 are never valid in BCD.
So the same number usually has a different bit pattern in BCD and in pure binary.

Same number, two different bit patterns.

Worked example: Encoding and decoding

(a) Write 738 in BCD. (b) What denary number is the BCD value 1001 0010 0101?

Have a go first?

Quick check

Fill in the blanksQuestion 1 · Recall

Denary 46 in BCD is

CalculateQuestion 2 · Recall

What denary number does the BCD value 0110 0001 0111 represent?

Multiple choiceQuestion 3 · Apply

Each byte below is meant to hold two BCD digits. Which one cannot be valid BCD?

A1001 0011B0101 1010C0000 0001D1000 1000

Answer the 3 questions above to continue.