Unused BCD codes

Also called: invalid BCD codes, BCD don't-cares, BCD don't cares, unused BCD combinations

In 4-bit BCD only 0000 to 1001 (digits 0 to 9) occur, so codes 1010 to 1111 (minterms 10 to 15) are don't-cares when simplifying BCD circuits.

Binary-coded decimal (BCD) stores each decimal digit 0 to 9 in four bits, 0000 to 1001. Four bits have 16 patterns, so six of them, 1010 to 1111, are never used.

When a circuit's input is a BCD digit, those six inputs simply never arrive. The output for them doesn't matter, so they become don't-cares, written d(10, 11, 12, 13, 14, 15) or d(10–15).

On a four variable k map the unused codes sit in a tidy block:

the whole AB = 11 row: m12, m13, m15, m14
the right half of the AB = 10 row: m11 and m10

Because they are next to so many cells, these X's often let small groups double or quadruple in size. A function that needs several 3- or 4-literal terms without them may shrink to one or two short terms.

This is why BCD circuits, such as the decoder for a 7-segment display or the logic in a bcd counter, are classic K-map exercises.

AB\CD	00	01	11	10
00	0m0	0m1	0m3	0m2
01	0m4	0m5	0m7	0m6
11	Xm12	Xm13	Xm15	Xm14
10	1m8	1m9	Xm11	Xm10

Worked examples

Example

Digit is 8 or 9

F = 1 when a BCD digit is 8 or 9: F = Σm(8, 9), d(10–15), shown above.

1.
The 1s are m8 and m9, in the bottom row.
2.
The X's fill the rest of the bottom row and the whole AB = 11 row.
3.
Together they make a group of 8: rows 11 and 10, where A = 1. F = .
4.
Without the don't-cares, the best you could do is .

Example

Digit is 2, 3, 6 or 7

Simplify F = Σm(2, 3, 6, 7), d(10–15).

AB\CD	00	01	11	10
00	0m0	0m1	1m3	1m2
01	0m4	0m5	1m7	1m6
11	Xm12	Xm13	Xm15	Xm14
10	0m8	0m9	Xm11	Xm10

1.
The 1s fill columns CD = 11 and 10 in the top two rows.
2.
The X's m15, m14, m11, m10 complete those two columns in the bottom two rows.
3.
Group all 8 cells of the right half: C = 1. F = .
4.
Without the X's, the answer would be .

Common mistakes

Treating the unused codes as 0s, which throws away an easy simplification.
Circling a group made only of X's. It covers no real 1s, so it adds a useless term.
Placing the unused codes in the wrong cells. Row AB = 10 holds m8 m9 m11 m10, so only its right half is unused.

Practice Unused BCD codes

Interactive questions with instant feedback and a worked solution for every wrong answer.

Karnaugh Maps lesson full course

A BCD digit ABCD (0–9) drives F = 1 when the digit is 5 or more. F = Σm(5, 6, 7, 8, 9) with don't-cares d(10–15). Circle a minimal set of groups.

Practice exams

Learn it step by step

Unused BCD codes is taught in Karnaugh Maps and Combinational Logic.

Karnaugh Maps →Combinational Logic →

All terms