Unsigned binary represents only zero and positive integers. With n bits, the range is zero through 2^n − 1. Addition follows the usual column method, except each column carries when its total reaches two instead of ten.
Worked example
Add 0101 and 0011 using four bits. The rightmost 1 + 1 produces 0 with a carry. Carrying through the next columns gives 1000, which is decimal 8. Adding 1111 and 0001 instead needs five bits: 10000.
What to watch for
A fixed-width result can discard the final carry and wrap around. Decide whether the circuit must report that carry or retain an extra result bit.
Try it yourself
What is the largest unsigned value in six bits?
Answer: 2^6 − 1 = 63. Adding one produces 64, requiring a seventh bit; a six-bit result wraps to zero.
How to study this topic
Write the base and bit width beside every value. Expand place weights before using a shortcut, then convert your answer back to decimal as an independent check. Representation and value are different ideas.
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Digital Electronics