A Decimal to Binary Coded Encoder has _____ inputs and _____ outputs.

An encoder is a combinational logic circuit that converts exactly one active input line, out of N mutually exclusive input lines, into a corresponding coded binary output. For the output code to uniquely represent every input line, the number of output bits n must satisfy 2n ≥ N.

1. A decimal digit has 10 possible values (0 through 9), so an encoder built for decimal digits needs exactly 10 input lines — one dedicated line per digit.

2. The smallest bit-width n for which 2n ≥ 10 is n = 4, because 23 = 8 is too small to cover all ten digits while 24 = 16 comfortably covers them; hence the encoder needs 4 output lines.

3. For example, activating the input line for digit 5 forces the 4-bit output to the BCD code 0101, and activating the line for digit 9 forces the output to 1001 — each of the 10 input lines maps to its own unique 4-bit code.

Checking the bound both ways confirms the count: 23 = 8 < 10 (so 3 bits are not enough) and 24 = 16 ≥ 10 (so 4 bits suffice), which fixes the encoder at 10 input lines and 4 output lines.