Boolean logic: A . B + C

The idea

This row gives a Boolean expression written with standard notation: A . B + C. The dot means AND, the plus means OR, and the letters A, B and C are Boolean inputs that each take the value 0 or 1. Operator precedence matters: the AND (dot) binds more tightly than the OR (plus), so the expression is read as (A AND B) OR C, not as A AND (B OR C). Work it out by evaluating A . B first, then OR-ing that result with C. For example, if A = 1, B = 0 and C = 1, then A . B = 0, and 0 + 1 = 1, so the whole expression is 1. If A = 1, B = 1 and C = 0, then A . B = 1, and 1 + 0 = 1. A multiple-choice question will test whether you apply that precedence correctly and can substitute input values accurately.

What earns the marks

• Recognises that the dot symbol represents the AND operation and the plus symbol represents the OR operation.
• Applies precedence so that A . B is evaluated before the OR with C, giving (A AND B) OR C.
• Correctly substitutes given input values for A, B and C and evaluates the AND part first.
• Combines the AND result with C using OR to reach the final 0 or 1 output.
• Rejects the misreading A AND (B OR C) when the correct grouping is (A AND B) OR C.

Common mistakes and how to put them right

• Reading the expression left to right and OR-ing B with C first.

  Put it right: AND binds more tightly, so A . B is evaluated before the OR with C.

• Treating the dot as multiplication of numbers rather than the logical AND of Boolean values.

  Put it right: Inputs are 0 or 1 and the dot is AND.

• Forgetting that OR gives 1 when either input is 1.

  Put it right: 0 + 1 and 1 + 0 both give 1, and only 0 + 0 gives 0.

Exam tips

• Write the bracketed form (A AND B) OR C beside the expression before substituting values, so precedence is fixed.
• Evaluate the AND term on its own line, then combine with C, to avoid mixing the two operations.
• Check each substitution against the truth values 0 and 1 rather than guessing the final answer.