Decoder

n-to-2n decoder — selects exactly one output line based on the binary input.

Inputs
A
B
C
→
Binary010= 2
Outputs — Y2 is active
Y00
Y10
Y21
Y30
Y40
Y50
Y60
Y70
Block Diagram
3-to-8DecoderA=0B=1C=0Y0=0Y1=0Y2=1Y3=0Y4=0Y5=0Y6=0Y7=0
Minterm Logic
Y0 = A' · B' · C' = 0
Y1 = A' · B' · C = 0
Y2 = A' · B · C' = 1
Y3 = A' · B · C = 0
Y4 = A · B' · C' = 0
Y5 = A · B' · C = 0
Y6 = A · B · C' = 0
Y7 = A · B · C = 0
Truth Table
ABCY0Y1Y2Y3Y4Y5Y6Y7
00010000000
00101000000
01000100000
01100010000
10000001000
10100000100
11000000010
11100000001
About the Decoder
A 3-to-8 decoder takes 3 binary inputs and activates exactly one of 8 output lines. Each output Yi corresponds to a unique minterm — an AND of all inputs where each variable is either in true or complemented form. Decoders are fundamental building blocks used in memory address selection, instruction decoding, and implementing arbitrary combinational logic (any Boolean function can be built with a decoder + OR gate).