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Digital Logic

Build a digital combination lock with logic gates

A combination lock made of logic gates opens for one setting of its switches and stays shut for every other. For four switches A, B, C and D and the code 1 0 1 1, the rule is OPEN = A · B̄ · C · D: an AND of all four, with a NOT on every switch that must be 0. Built from 2-input gates, that's one NOT and three ANDs.

A11B00C11D11gatesANDs and a NOTOPENfifteen settings keep it shut; one opens it
The lock: four switches, and OPEN lights for exactly one of the sixteen settings, 1 0 1 1

Write the rule from the code

An AND outputs 1 only when every input is 1. The switches that should be on, A, C and D, can go straight in. B should be off, so it goes through a NOT first: NOT B is 1 exactly when B is 0. Now all four AND inputs are 1 for the code, and at least one is 0 for anything else.

OPEN = A · B̄ · C · D

Chain the ANDs

Each AND here takes two inputs, so combine the four signals two at a time:

  1. AND A with NOT B
  2. AND C with D
  3. AND those two results, and wire the output to the OPEN light

Three ANDs and one NOT. Chaining them in a line, ((A · B̄) · C) · D, works just as well and uses the same three gates.

Live experiment

Crack the code

Four switches, A to D, and a vault that opens for 1 0 1 1 only. The door shows the four inputs of the AND that opens it: A, NOT B, C and D. B's lamp is lit when B is off. Get all four lit and the door swings open.

Try it yourself: free lesson

“Project: Combination lock” is the project that ends Gate Grove, Digital Logic World 1. Free with an account. Lessons unlock in order, so you’ll do the 6 before it first.

Test all sixteen

Four switches give 2⁴ = 16 settings, so the truth table has 16 rows with a single 1. Test the code first: OPEN should light. Then test the four near misses, each one switch away from the code: 0011, 1111, 1001 and 1010. Every one must stay dark. A near miss that opens means that switch's wire never reached the ANDs.

SettingOPEN
1011, the code1
0011, 1111, 1001, 10100
the other 110

Make the code settable

A lock you can't re-code isn't much use. Add four code switches, K1 to K4, and compare each lock switch with its code switch using an XNOR gate, which outputs 1 when its two inputs match. AND the four XNOR outputs together and OPEN lights whenever every switch matches its code switch, whatever the code is.

To build it for real, a 74HC08 has four 2-input ANDs and a 74HC04 has six NOTs. Pull each switch input to a definite level with a resistor, so an open switch reads 0 instead of floating.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Project: Combination lock” is the project that ends Gate Grove, Digital Logic World 1. Free with an account. Lessons unlock in order, so you’ll do the 6 before it first.

Or start from the very first lesson, no account needed

Practice questions

Three quick questions from the lessons. Pick an answer to check it.

  1. Question 1 of 3AND gates here have two inputs. To AND three signals together you need…
    Show the answer

    Answer: Two AND gates, one feeding the other. AND the first two, then AND that result with the third. The output of one gate is just a wire, and it can feed another gate.

    • Why not “Three AND gates”? Three gates is one more than needed: AND two signals, then AND that result with the third.
    • Why not “A NOT gate”? A NOT flips one signal; it can't combine them. Combining three takes two ANDs.
    • Why not “One AND gate with a spare wire”? A 2-input AND has room for two signals only. Leaving a wire spare would leave the third signal out of the rule.
  2. Question 2 of 3A truth table for three inputs has how many lines?
    Show the answer

    Answer: 8. 2 × 2 × 2.

    • Why not “3”? 3 is the number of inputs. Each can be 0 or 1, so the combinations multiply to 8.
    • Why not “6”? Each input doubles the lines, so three inputs give 2 × 2 × 2 = 8, not 6.
    • Why not “9”? 9 would be 3 × 3, but each input has only two values, so it's 2 × 2 × 2 = 8.
  3. Question 3 of 3LOAD is opcode 00. The LOAD line's AND takes…
    Show the answer

    Answer: NOT OP1 and NOT OP0. LOAD is opcode 00: both bits must be 0, so both go through a NOT first.

    • Why not “OP1 and OP0”? OP1 and OP0 are both 1 only for opcode 11, so that AND picks out HALT, not LOAD.
    • Why not “NOT OP1 and OP0”? NOT OP1 and OP0 is 1 for opcode 01, ADD. For 00, both bits go through a NOT.
    • Why not “OP1 and NOT OP0”? OP1 and NOT OP0 is 1 for opcode 10, JUMP. LOAD's 00 needs a NOT on both bits.
Keep practising: free lesson

“Project: Combination lock” is the project that ends Gate Grove, Digital Logic World 1. Free with an account. Lessons unlock in order, so you’ll do the 6 before it first.

Questions people ask

How do I change the lock's code?

In the fixed version, move the NOT gates: one goes on every switch that must be 0. For a settable lock, compare each switch with a code switch using an XNOR gate, which gives 1 when the two match, then AND the four XNOR outputs together.

How secure is a 4-bit combination lock?

Not very: there are only 16 settings, so trying them all takes a minute. Each extra switch doubles that, so 10 switches give 1,024. Real keypads add many more combinations, a delay or lockout after wrong tries, and a latch so the door stays open.

Why does the lock open when I flip extra switches?

That switch isn't really in the ANDs. If changing it never changes OPEN, its wire is missing or goes to the wrong gate. Test the code, then every setting one switch away from it: all four near misses must stay shut.

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