Logic circuit to handle incrementing by 1

Question

You can use cascaded full adders to add any two binary numbers together. Is there a circuit for when I only want to add 1 (incrementing the value)? Is there a similar circuit for subtracting (i.e. adding 0b1111 1110)? I'm working with 8 bit numbers, but this applies for all word lengths.

Answer 1

Let's see. In a simple ripple carry adder, sum,carry-out = a + b + carry-in

c[0] = carry-in
for i in n
    sum[i] = a[i] ^ b[i] ^ c[i]
    c[i+1] = (a[i]&b[i]) | (a[i]&c[i]) | (b[i]&c[i])
carry-out = c[n]

Now if we want to compute sum,carry-out = a + 0 + 1, set b[] = all 0 and simplify:

c[0] = 1
for i in n
    sum[i] = a[i] ^ c[i]
    c[i+1] = a[i] & c[i]
carry-out = c[n]

which is simpler. Subtraction by 1 can be similarly simplified (exercise for reader: what is b[] and carry-in in that case?)

Happy hacking!

Answer 2

If you're talking about discrete logic, like 7400 series logic, then the chip you're looking for is called a counter. Two 74191 (4-bit up/down synchronous counter) chips cascaded will give you what you want, and there are other chips that do a similar function.

If you want the most compact way to add '1', then you could use half-adders for each bit instead of full adders. Not too sure about subtraction though.

Answer 3

What you are looking for is a edge triggered T-triggers. Input = output of previous stage AND count clock.

Here is schematics for transistor-based T-trigger:

http://forum.cxem.net/index.php?app=core&module=attach&section=attach&attach_rel_module=post&attach_id=45908