Q10Digital Electronics

Question

Express the number $(137)_{10}$ in BCD and binary.

Answer 1

We must mathematically expand the algebraic equation $(23)_{x} + (12)_{x} = (101)_{x}$ strictly into its constituent polynomial terms based on powers of the unknown radix $x$ . This yields: $(2 x^{1} + 3 x^{0}) + (1 x^{1} + 2 x^{0}) = (1 x^{2} + 0 x^{1} + 1 x^{0})$ . Simplifying: $2 x + 3 + x + 2 = x^{2} + 1$ . Thus, $3 x + 5 = x^{2} + 1$ , which algebraically rearranges to the quadratic equation $x^{2} - 3 x - 4 = 0$ . Factoring yields $(x - 4) (x + 1) = 0$ . Since a number base physically cannot be negative, $x = 4$ .

Q10Digital Electronics

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