is there any simple circuit that can perform the all basic binary
arithmetic operations (multiplication, division, subtraction, addition)?
Depends on what you call 'simple'. If you want to do these operations
on four-bit binary numbers, you could put a lookup table in ROM
that takes
4 bits of operand 1
4 bits of operand 2
2 bits of identify-the-operation code
and outputs up to eight bits (enough for multiply to not overflow)
You'll have to decide how to treat negative results in subtraction.
Division can yield four bits of result and four more of remainder
and the whole thing is a single ROM of 1024 bytes (this is VERY small
chip, really just a fraction of a current sizes). So, if less than
one IC
counts as simple, this is simple.
But, such a ROM has thousands of transistors; if you want to minimize
transistor count, consider that a modest op amp only needs a
dozen transistors, and that a transistor yields a current that is
proportional to the exponential of a voltage; you can do logarithms
with ease, and exponentials, and simple resistor connections
accomplish
sums (and negations are two-resistors-and-an-amplifier).
Up to 8 digits accuracy and maybe 1MHz bandwidth, you can
do all those operations on voltage-analog-to-pure-number signals
with maybe 150 transistors.
2 I/p nands of course.
