The AND-NOT gate

The AND-NOT gate

An AND-NOT gate calculates the function ‘A AND NOT B’. We have two different designs for this gate. The simpler appears in the first picture below. The lower input (which you’ll see is delayed slightly with respect to the upper one) is ‘A’, and the upper one ‘B’.

AND-NOT gate: simpler design

The easiest way to understand the operation of this gate is to ignore the upper input for a moment. The lower signal can simply pass through to the output; the ‘plus’ arrangement prevents the signal from propagating back along the B input. Now suppose that the three cells forming the horizonal bar of the plus are all electron heads. With the correct timing, this will block the flow of electrons from A.

An alternative design of AND-NOT gate is shown below.

AND-NOT gate: larger design

This design has two outputs. The upper output is giving us ‘A AND NOT B’, while the lower output is giving us ‘A OR B’. We could, of course, turn the gate upside-down to calculate the functions ‘A OR B’ on the upper output and ‘B AND NOT A’ on the lower.

If you look more closely at the gate, you’ll see that the only difference between the two outputs is in the presence or absence of an ‘ear’ - a single cell of copper sticking out of the gate next to the output wire. With the ear, the output gives the AND-NOT function; without it, the OR function. We could add ears to both outputs, in which case we will get both ‘A AND NOT B’ and ‘B AND NOT A’. The gate with both ears can function as a ‘broken crossover’: it will allow two signals to cross as long as they are never both ‘1’ at the same time. (A ‘working crossover’ can be constructed from three exclusive-OR gates, and is quite large: fortunately, however, the need for this can often be avoided in practice.)

Some other designs for elementary gates (including many of ours) and some other bits and pieces can be found, for example, here, here, here, et ici. A particularly good collection can be found at Nyles Heise’s website. Alan Tennant has several interesting designs, including ‘synchronised gates’ which can deal with signals arriving at any time.

Meanwhile, we’ll move on to more complicated things. By judicious placement of ears, let’s build a ROM.

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This page most recently updated Thu Aug 7 12:10:30 BST 2014
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