CS 101 Homework 6 - Challenge problem [up to 2 extra points]
Consider the two circuits shown below.
Both circuits take two 8-bit numbers A and B as input, i.e. the 16
bits A7...A0 and B7...B0, which appear along the top of the two
diagrams below. ('7' is the highest-order bit, and '0' the
lowest-order bit. For instance, if A = 19, which is 00010011 in
binary, then the bits A4, A1, and A0 are 1 and the others are 0.)
Each circuit is comprised of 8 identical subcircuits. Each subcircuit
takes just one pair of bits as input, e.g. A7 and B7. The subcircuits
also take input(s) from the left and produce output(s) to the right,
which become the input(s) of the next subcircuit. The final output(s)
of the right-most subcircuit are considered the output of the entire
circuit. The left-most inputs are held constant (to 0 or 1 as shown).
The contents of each subcircuit are shown in the dashed box
underneath. The small arrows on the wires indicate the flow of the
signals, i.e., from outputs to inputs.
(Note that the overall design is quite similar to the 4-bit adder from
the circuit lecture on
slide 19, which takes two 4-bit numbers as input, and is comprised of
4 identical subcircuits.)
- Determine the function of the circuit below. It has a
single output "R" (i.e., the output "Rout" of the right-most
subcircuit). What function does "R" compute, given any two 8-bit
numbers A and B as input? Note that each of the
8 subcircuits consists of one XNOR gate (i.e., an XOR followed by a NOT)
and one AND gate. Note also that the leftmost "Rin" input receives a
constant 1.
- Determine the function of the circuit below. It has
two outputs "P" and "Q" (i.e., the outputs "Pout" and "Qout" of the
right-most subcircuit). What function do "P" and "Q" compute, given
any two 8-bit numbers A and B as input? Note
that each of the 8 subcircuits consists of two OR gates, two 3-input
AND gates, and 4 NOT gates. Note also that the leftmost "Pin" and
"Qin" inputs receive a constant 0.
