I-gate

Question

How many 1*2 decoders are required to construct a 4*16 decoder?

Comments

$15$

Answer 1

$X$ $m*M$ decoder required to construct $n*N$

let $k = ceil(n/m)$

then $X=N/M + N/M^2 + N/M^3+ ........ + N/M^K$

Then according to question ::

$k=4/1 = 4$

$X = 16/2 + 16/2^2 + 16/2^3 + 16/2^4$

    $ = 8+4+2+1$

    $= 15$

OR other approch

Given 1*2 decoder

1 decoder -------- 2 lines

l line ------- 1/2 Decoder

16 lines   --- 16/2    = 8 Decoder

8 lines  ----- 8/2     =  4 Decoder

4 lines ----   4/2     = 2 Decoder

2 lines ----   2/2    = 1 Decoder

Total 15 decoder need