Digital Logic Tutorial

Binary Adder for 5 digits

This adder is made from 5 of the little adders in the last page. It can add a pair of numbers each between 0 and 31 and produce a result between 0 and 62. The inputs are the two boxes on the left. The number in the upper box is added to the number in the lower box and the result is displayed on the far right. Use the up and down arrows to change the numbers. You can only add numbers up to 31, since only 5 wires are hooked up: 11111 binary is 31 decimal.

If you stare at that long enough, you might start to see the paterns of how the logic works. You can go back to the simple full adder to see what is inside each box.

Digital logic math, we only have so many wires. When the total is more than the number of wires available, we call that an "overflow". In the circuit on this page, the overflow is just put into the display, so we can have a total which is more than the maximum input. 31+31=62.

Remember: It's all done with NANDs!

Next

Subtracting is NOT Adding (plus a bit)!

Or skip the math, and watch the 2 bit to 4 line active low decoder puts things in order.

Advanced

It should be easy to see how we could add more adders to build a circuit that would add 6, 7, 8 or more bit numbers together. Most computers today can add 32 bit numbers in a single operation; they have 32 bit adders. A 32 bit number can have a value between 0 and 4,294,967,296 (about 4 billion).

See also:

• http://ozark.hendrix.edu/~burch/cs/230/reading/09/3.html Flags, incrementers and ALU

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