LOGIC GATES IN COMBINATION

When you look at logic circuit diagrams for digital equipment, you are not going to see
just a single gate, but many combinations of gates. At first it may seem confusing and
complex. If you interpret one gate at a time, you can work your way through any network.
In this section, we will analyze several combinations of gates and then provide you with
some practice problems.

Figure 2-23 (view A) shows a simple combination of AND gates. The outputs of gates 1
and 2 are the inputs to gate 3. You already know that both inputs to an AND gate must be
HIGH at the same time in order to produce a HIGH output.

Figure 2-23. - Logic gate combinations: A. Simple combination of AND gates; B. Simple
combination of AND gates and OR gate.

The output Boolean expression of gate 1 is RS, and the output expression of gate 2 is
TV. These two output expressions become the inputs to gate 3. Remember, the output Boolean
expression is the result of the inputs, in this case (RS)(TV); spoken "quantity R AND
S AND quantity T AND V."

In view B we have changed gate 3 to an OR gate. The outputs of gates 1 and 2 remain the
same but the output of gate 3 changes as you would expect. The output of gate 3 is now
(RS)+(TV); spoken "quantity R AND S OR quantity T AND V."

In figure 2-24 (view A), the outputs of two OR gates are being applied as the input to
third OR gate. The output for gate 1 is R+S, and the output for gate 2 is T+V. With these
inputs, the output expression of gate 3 is (R+S)+(T+V).

Figure 2-24. - Logic gate combinations: A. Simple combination of OR gates; B. Simple
combination of OR gates and AND gate; C. Output expression without the parentheses.

In view B, gate 3 has been changed to an AND gate. The outputs of gates 1 and 2 do not
change, but the output expression of gate 3 does. In this case, the gate 3 output
expression is (R+S)(T+V). This expression is spoken, "quantity R OR S AND quantity T
OR V." The parentheses are used to separate the input terms and to indicate the AND
function. Without the parentheses the output expression would read R+ST+V, which is
representative of the circuit in view C. As you can see, this is not the same circuit as
the one depicted in view B. It is very important that the Boolean expressions be written
and spoken correctly.

The Truth Table for the output expression of gate 3 (view B) will help you better
understand the output. When studying this Truth Table, notice that the only time f is HIGH
(logic 1) is when either or both R and S AND either or both T and V are HIGH (logic 1).

R |
S |
T |
V |
f |

0 |
0 |
0 |
0 |
0 |

0 |
0 |
0 |
1 |
0 |

0 |
0 |
1 |
0 |
0 |

0 |
0 |
1 |
1 |
0 |

0 |
1 |
0 |
0 |
0 |

0 |
1 |
0 |
1 |
1 |

0 |
1 |
1 |
0 |
1 |

0 |
1 |
1 |
1 |
1 |

1 |
0 |
0 |
0 |
0 |

1 |
0 |
0 |
1 |
1 |

1 |
0 |
1 |
0 |
1 |

1 |
0 |
1 |
1 |
1 |

1 |
1 |
0 |
0 |
0 |

1 |
1 |
0 |
1 |
1 |

1 |
1 |
1 |
0 |
1 |

1 |
1 |
1 |
1 |
1 |

f = (R+S) (T+V)

Now let's determine the output expression for the NOR gate in figure 2-25. First write
the outputs of gates 1, 2, and 3:

Figure 2-25. - Logic gate combinations.

Since all three outputs are applied to gate 4, proceed as you would for any NOR gate.
We separate each input to gate 4 with an OR sign (+) and then place a vinculum over the
entire expression. The output expression of gate 4 is:

The Truth Table shown below is only for gate 4.

When you are trying to determine the outputs of logic gates in combination, take them __one
gate at a time!__

*
**Now write the output expressions for the following logic gate combinations*:

Q.27

Q.28

Q.29

Q.30

Q.31

Q.32