binary arithmetic

Question 1

Binary addition

Answer 1

0+0=0
0+1=1
1+0=1
1 + 1 = 0 with carry
Carry + 0 + 0 = 1
Carry + 0 + 1 = 0 with carry
Carry + 1 + 0 = 0 with carry
Carry + 1 + 1 = 1 with carry

Question 2

Binary Subtract

Answer 2

0−0=0
0 − 1 = 1 with a borrow
1−0=1
1−1=0
0 − 0 − borrow = 1 with a borrow
0 − 1 − borrow = 0 with a borrow
1 − 0 − borrow = 0
1 − 1 − borrow = 1 with a borrow

Question 3

Binary multiplication

Answer 3

like with decimal, but with shifting the result every time and having an addition of the partial results.

Question 4

Modulo-N counters

Answer 4

Number sequences starting from zero to MAX_VALUE:
0 .. 1..2..Nmax-1.. 0 .. 1.. 2 and then again starting from zero. (like transaction log id):

cntr = (cntr + 1 ) % n;
cntr = (cntr + 1) & 0x3f;