Some basic question about Digital Circuits

[isaacnewton]

(1) The attached is the Truth Talbe of a 4-bit ALU. I have a simple
question about it. Please look the circled expression: (A+B) plus AB
(Bar). What's the difference between '+' and 'plus'? Are they the
same? If they are same, why the author use different notations?

(2) The Logic Diagram of the ALU is also attached. From the figure,
we can see, the Carry in bit Cn and Carry out bit Cn+4 are
Active Low, and all the others are Active High.
What's the advantage of using some Active Low and some Active High
input/output?

(3) If I want to use TSMC 0.18 um
https://www.mosis.com/Technical/Testdata/tsmc-018-prm.html
to realize the ALU, how much of target Propogation Delay is
reasonable?

Thank you very much.

 

[flatulent]

The two columns to the right are in two different notations. The far right is standard algebra and English language as spoken by math professors. Notice the top of the column says true is a low voltage level. The next one over is logic.

In the logic notation, letters next to each other are AND. The + sign is OR. The + sign with a circle around it is XOR (exclusive OR). The over-bar is NOT.

Your best bet is to follow the two superscripts to the bottom of the sheet and read the details.

As far as why some are active high and some active low, the chip is designed for combining with others to make a word several times 4 bits wide. One of the main time delays is for the carry to propagate through. Therefore minimizing the number of gates in the signal path is desirable. Had all signals been high true, there would be more gates required.

 

[zzczx]

The two columns to the right are in two different notations. The far right is standard algebra and English language as spoken by math professors. Notice the top of the column says true is a low voltage level. The next one over is logic.

In the logic notation, letters next to each other are AND. The + sign is OR. The + sign with a circle around it is XOR (exclusive OR). The over-bar is NOT.

Do mean that (a+b) plus ab(bar) is equal to (a OR b ) plus (a and b(bar))?

 

[hahaguy2]

(1) The attached is the Truth Talbe of a 4-bit ALU. I have a simple
question about it. Please look the circled expression: (A+B) plus AB
(Bar). What's the difference between '+' and 'plus'? Are they the
same? If they are same, why the author use different notations?

+ is logical "OR" which means:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1
plus is the mathematical ADD which means:
0 PLUS 0 = 0
0 PLUS 1 = 1
1 PLUS 0 = 1
1 PLUS 1 = 10