Make Electronics

Experiment 19: Learning Logic

186 Chapter 4

essentIAls

Logic   gate    basics

The NAND gate is the most fundamental building block of digital computers,

because (for reasons which I don’t have space to explain here) it enables digital

addition. If you want to explore more try searching online for topics such as

“binary arithmetic” and “half-adder.”

Generally, there are seven types of logic gates:

• AND


• NAND
  
  
  • OR
  
  
  • NOR
    
    
    • XOR
    
    
    • XNOR
      
      
      • NOT
      
      
      
      
    
    
    
    
  
  
  
  

Of the six two-input gates, the XNOR is hardly ever used. The NOT gate has a

single input, and simply gives a negative output when the input is positive or a

positive output when the input is negative. The NOT is more often referred to as

an “Inverter.” The symbols for all seven gates are shown in Figure 4-56.

INVERTER

AND NAND OR XOR

NOT

Logical Inputs

Logical Outputs

NOR XNOR

Figure 4-56. American symbols for the six types of two-input logic gates, and the

single-input inverter.

I’ve shown the American symbols.

Other symbols have been adopted in

Europe, but the traditional symbols

shown here are the ones that you will

usually find, even being used by Eu-

ropeans. I also show the truth tables,

in Figure 4-57, illustrating the logical

output (high or low) for each pair of

inputs of each type of gate.

Figure 4-55. Ann and Bob attempt to over-
come the limitations of Boolean logic.

Figure 4-57. Inputs and corresponding outputs for the six types of logic gates (note

that the XNOR gate is seldom used). The minus signs indicate low voltage, close

to ground potential. The plus signs indicate higher voltage, close to the positive

potential of the power supply in the circuit. The exact voltages will vary depending

on other components that may be actively connected.