I've never learned how to do binary arithmetic and was wondering if there was a straightforward technique to doing the following things in your head:

  1. Add bits.
  2. Concatenate bits.
  3. Read bit values into decimal form.

For (1), just being able to do:

+   101

For (2), instead of add, concatenate:

101011 + 101 = 101011101 ? how to determinal decimal value

What I'm doing now is starting from the right, just walking through the bits until I get to about #4 and it gets too complicated lol. I go 00 = 0, 01 = 1, 10 = 2, 11 = 3, ..?.


For 1, you are just adding with carry like in base $10$. Start from the bottom and add each column. For 2, just recite one number after the other. For 3, it helps to memorize the powers of $2$. A fair number of people know them at least up to $2^{16}=65536$. Then you have to add in base $10$ the powers that have a $1$ in them. I would start from the least significant bit as the numbers stay small longer, but I don't know of a royal road. For your example $101011101=1+4+8+16+64+256=349$ where I did the addition in my head. It helped to have the number written down so I could point at it and keep my place. It also helps not to have to compute that the highest bit is worth $256$.


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