Fundamentals of digital electronics. Prepared by - Anuradha Tandon Assistant Professor, Instrumentation & Control Engineering Branch, IT, NU. Why go digital?. Analogue signal processing is achieved by using analogue components such as: Resistors.
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Prepared by - AnuradhaTandon
Instrumentation & Control Engineering Branch,
– Represents a value (0 or 1), Three variables: a, b, and c
– Appearance of a variable, in true or complemented form
– Nine literals: a’, b, c, a, b, c’, a, b, and c
• Product term
– Product of literals, Four product terms: a’bc, abc’, ab, c
• Sum‐of‐products (SOP)
– Above equation is in sum‐of‐products form.
– “F = (a+b)c + d” is not.
F(A, B, C) = A’BC + BC’ + AB
F(A, B, C) = (A + B’ + C’).(B’ + C).(A’ + B’)
F(X,Y,Z) = XZ+Y’Z+X’YZ
can be represented using 2-input AND and OR gates as shown in the Fig. 1:
Fig. - 1
can be represented using 2-input AND and OR gates as shown in the Fig. 2:
Fig. - 2
a form that:
– Allows comparison for equality.
– Has a correspondence to the truth tables
– Sum of Minterms (SOM)
– Product of Maxterms (POM)
Example: x’y’, xz, xyz, …
Example: F(x,y,z) has 8 minterms
x’y’z’, x’y’z, x’yz’, ...
Example: x’y’z’ = 1 only when x=0, y=0, z=0
XY (both normal)
XY’ (X normal, Y complemented)
X’Y (X complemented, Y normal)
X’Y’ (both complemented)
X+Y (both normal)
X+Y’ (x normal, y complemented)
X’+Y (x complemented, y normal)
X’+Y’ (both complemented)
• The sum of minterms
• The product of maxterms
• Σmi – for all minterms that produce 1 in the table,
• ΠMi – for all maxterms that produce 0 in the table
= A C+A D+BC+BCD
F = AB + CD
= ( A+C)(B+C)(A+D)(B+D)
–The K‐map method is easy and straightforward
–A graphical method of simplifying logic equations or truth tables
-Also called a K map
A’B’, A’B, AB, AB’
00, 01, 11, 01
F =A’B’ + A’B = A’ F = A’B + AB = B
– Output depends on present input
– Examples: F (A,B,C), FA, HA, Multiplier, Decoder, Multiplexor, Adder, Priority Encoder
Y = F (a,b)
– Receptionist Ask: Which Dept. to Go ?
– Receptionist Redirect you to some building according to your Answer.
• N input: 2N output
• Memory Addressing
– Address to a particular location
S(x,y,z)= Σ(1,2,4,7) , C(x,y,z)=Σ(3,5,6,7)
• Functions S and C can be implemented using a 3‐to‐8 decoder and two 4‐input OR gates
– Routes one of its N data inputs to its one output, based on binary value of select inputs
– Like a rail yard switch
• Stores bits, also known as having “state”
• Simple example: a circuit that counts up in binary
– Press call: light turns on
• Stays on after button released
– Press cancel: light turns off
– Logic gate circuit to implement this?
– Does the right S Q circuit on do what we want?
• No: Once Q becomes 1 (when S=1), Q stays forever – no value of S can bring back to 0