Logic Pull Up resistors

[Jbliss]

Hi
I have just started learning simple logic using 4011's and 74hc02 (parts i had available). and I have a question is it nessiscary to use pull up resistors on the input always. so far I have had no such luck with out them.
Could i be doing something wrong. 
Some circuits Show with out them

Thanks Josh 
 

[SeanB]

If using with a switch yes, if using from the output of another IC no. Pull up for CMOS is very forgiving, you can use from 220R to 1M at low speed, though you probably will want to stick to around 2-10k for most cases. Connect unused inputs to a power rail via a 10-100k resistor, otherwise they will float and may oscillate.

[Jbliss]

Thank You. 

[Jbliss]

Just another question whats the largest number for a 4 bit adder

[matseng]

Just another question whats the largest number for a 4 bit adder

Mmmm? 15  Unless you use more than one 4-bit adder in conjunction - then it might be 255,  4095,  65535,  1 048 575, 16 777 215, 268 435 455 or 4 294 967 295 for 2,3,4,5,6,7 or 8 of the adders ganged up.

This is for unsigned numbers. If you want to process both negative and positive numbers you have to divide those values by two.

[Jbliss]

https://izatxamir.files.wordpress.com/2010/02/4-bit-full-adder.jpeg

for a circuit like this highest number ?

[matseng]

It can add two 4-bit numbers each ranging from 0 to 15. And return a number between 0 and 31 since the CarryOut can be considered a 5th output bit.

[Jbliss]

Thank You 
merry christms