Question

Determine the check digit for the UPCs that have these initial 11 digits. a) 73232184434 b) 63623991346 c) 04587320720 d) 93764323341

Answer 1

The check digits

a) x₁₂ ≡ 5( mod 10 )

b) x₁₂ ≡ 2( mod 10 )

c) x₁₂ ≡ 0( mod 10 )

d) x₁₂ ≡ 3( mod 10 )

Explanation:

Given the data in the question;

We know that the formula for determining the UPCs check is;

3x₁ + x₂ + 3x₃ + x₄ + 3x₅ + x₆ + 3x₇ + x₈ + 3x₉ + x₁₀ + 3x₁₁ + x₁₂ ≡ 0( mod 10 )

now we will substitute the given values to determine the value of the last bit

a)

73232184434

we substitute into the formula

3×7 + 3 + 3×2 + 3 + 3×2 + 1 + 3×8 + 4 + 3×4 + 3 + 3×4 + x₁₂ ≡ 0( mod 10 )

x₁₂ ≡ 5( mod 10 )

b)

63623991346

we substitute into the formula

3×6 + 3 + 3×6 + 2 + 3×3 + 9 + 3×9 + 1 + 3×3 + 4 + 3×6 + x₁₂ ≡ 0( mod 10 )

x₁₂ ≡ 2( mod 10 )

c)

04587320720

we substitute into the formula

3×0 + 4 + 3×5 + 8 + 3×7 + 3 + 3×2 + 0 + 3×7 + 2 + 3×0 + x₁₂ ≡ 0( mod 10 )

x₁₂ ≡ 0( mod 10 )

d)

93764323341

we substitute into the formula

3×9 + 3 + 3×7 + 6 + 3×4 + 3 + 3×2 + 3 + 3×3 + 4 + 3×1 + x₁₂ ≡ 0( mod 10 )

x₁₂ ≡ 3( mod 10 )