Express a truth table using a single if-condition

Question

My code looks like this:

/*
 * A B
 * 0 0 -> 1
 * 0 1 -> 0
 * 1 0 -> 0
 * 1 1 -> 0
 */

#define A condition_1
#define B condition_2

if (A) {
    // do nothing
} else {
    if (B) {
        // do nothing
    } else {
        // do something
    }
}

Above I've reported the truth table for two conditions where 1 is true and 0 is false, is there a way to express the truth table into a single if-condition?

`if (A && !B) { do something }` – RbMm Mar 21 '20 at 22:02 — RbMm, Mar 21 '20 at 22:02

score 5 · Accepted Answer · answered Mar 21 '20 at 22:05

5

Your truth table represents a NOR (not or) operation. You can get that easily by combining logical NOT (!) with logical OR (||)

if (!(A || B)) {

}

PS. Please, don't use #define macros. It's very error-prone and tends to bite programmers who use it. Most often there are safer and more readable ways to perform what macro does.

answered Mar 21 '20 at 22:05

Yksisarvinen

18,008
2
24
52

DeMorgan for the win! – user4581301 Mar 21 '20 at 22:27

score 4 · Answer 2 · answered Mar 21 '20 at 22:07

4

Use:

if (!A && !B) {
    // do something
}

Think, your truth table only returns 1 when both conditions are false (0 0 -> 1). You can use ! in both to invert it.

answered Mar 21 '20 at 22:07

Ronaldd

56
3

score 1 · Answer 3 · answered Mar 21 '20 at 22:19

If there is only one 1 in the table then it's essentially AND operation. If there is only one 0 then it's OR operation. If there are two of both then you can make it an equality operation.

When you know which operation to chose your next step is to figure out which operands should be negated. For AND both operands must turn to 1 to produce 1 (1 AND 1 = 1), so negate those who would otherwise produce 0. For OR it's opposite, negate those who would produce 1 when trying to have 0 a s result (0 OR 0 = 0)

For equality operation bear in mind that bool can either be true or false, so there are only two values. If you try to use something that is not a bool for a logical operand then there would be problems. With that in mind when you want to produce equality negate any of the operands if originally they don't produce correct result (0 == 0 = 1 and also 1 == 1 = 1, if you understand me).

In your particular case we have only one 1 in the table so it's an AND operation. Both operands are 0 for this 1 outcome so we have to negate both of them:

!A && !B

Express a truth table using a single if-condition

3 Answers3