Hello,

I need to build a device that accepts a 4-bit number and deciphers whether it's ascending, or descending (or both, such as 0000 or 1111.) The device has two outputs. The first gives 1 if and only if the number is ascending (each bit is greater than or equal to the bit to its left.), the other when it is descending.
For example:
0000
0001
0011
0111
1111

are all examples for ascending numbers, whereas;

0000
1000
1100
1110
1111

are all descending. The rest are neither one.

The design needs to include minimum number of logic gates!
gates allowed (AND,OR,NAND,NOR,XOR).

I have managed to create it using 12 gates. Can anyone come up with less?

I would really be glad for help!

 

Can you post your work for it to be commented upon?

 

Try it with only NAND and NOR, as those are often the only ones available in CMOS circuits.

 

Here's my work (also all input/output)

can you find a more efficient circuit to produce the exact same output?