Help please, I am new to circuits and decoders and I need some serious help.
How to build a 4×16 decoder using ONLY two 2×4 decoders?
Following the steps we took in the lecture, we are supposed to build a 4×16 decoder. So here taking k to be 4, k is even, so we will have \$2^k\$ so \$2^4 = 16\$ AND gates & 2 decoders each of size \$2^{k/2}\$ so \$2^2 = 4\$.
So we have 16 AND gates & two 2×4 decoders. Each 2×4 decoder has 4 AND gates so we have 8 AND gates that should be connected to the 16 AND gates, how do I do that?
Best Answer
A \$2\$-by-\$4\$ decoder has two input lines and four output lines, only one of which is logical \$1\$ at any time. Which line is \$1\$ depends on the input bit pair which can be \$00, 01, 10, 11\$.
So take two such \$2\$-by-\$4\$ decoders which give you four input lines. Let the output lines be \$a_0, a_1, a_2, a_3\$ for one decoder and \$b_0, b_1, b_2, b_3\$ for the other. Use the \$16\$ AND gates to compute the \$16\$ functions \$ a_i \wedge b_j, 0 \leq i \leq 3, 0 \leq j \leq 3\$. We now have a \$4\$-by-\$16\$ circuit with the property that only one output is a logical \$1\$ at any time: which one depends on the values of $i$ and $j$ which in turn depend on the \$4\$ input bits. In other words, we have a \$4\$-by-\$16\$ decoder constructed from two \$2\$-by-\$4\$ decoders and \$16\$ AND gates.