Boolean Algebra (Binary Logic)
Theorem
A+0=A
A+1=1
A+A=A
A + A’ = 1
A*0=0
A*1=A
A*A=A
A * A’ = 0
A+B=B+A
(A + B) + C = A + (B + C)
AB + AC = A(B + C)
A*B=B*A
(A * B) * C = A * (B * C)
(A + B)*(A
B) (A + C) = A + BC
Boolean Algebra (Binary Logic)
A’B’ + A’B + AB = A’ + B = Z
A’
B’
=>
A’
B
Z
A’
B
Z
A
B
A+0=A
A+1=1
A+A=A
A + A’ = 1
A*0=0
A*1=A
A*A=A
A * A’ = 0
A+B=B+A
(A + B) + C = A + (B + C)
AB + AC = A(B + C)
A*B=B*A
(A * B) * C = A * (B * C)
(A + B)*(A + C) = A + BC
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’
(A * B)’ = A’ + B’
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’
(A * B)’ = A’ + B’
A
B
A
B
AB + AC
A
C
AB + AC
A
C
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’
(A * B)’ = A’ + B’
Why NAND and NOR gates?
Why NAND and NOR gates?
A
B
A
B
AB + AC
A
C
AB + AC
A
C
Boolean Algebra (Binary Logic)
More Function (Exclusive‐OR)
Z = AB’ + A’B
Boolean Algebra (Binary Logic)
More Function (Exclusive‐OR)
Z = AB’ + A’B
Z=A
A
B
B
Z
Boolean Algebra (Binary Logic)
More Function (Exclusive‐OR)
Z = AB’ + A’B
Z=A
A
B
A
B’
Z
A’
B
B
Z
Boolean Algebra (Binary Logic)
Parity circuits: even/odd
Z
ASCII Table (7-bit)
(ASCII = American Standard Code for Information Interchange)
Decimal
-------
Octal
-----
Hex
---
Binary
------
Value (Keyboard)
-----
ASCII Table (7-bit)
(ASCII = American Standard Code for Information Interchange)
Decimal
-------
Octal
-----
Hex
---
Binary
------
Choi = $43 $68 $6F $69
Value (Keyboard)
-----
ASCII Table (7-bit)
(ASCII = American Standard Code for Information Interchange)
Decimal
-------
Octal
-----
Hex
---
Binary
------
Choi = $43 $68 $6F $69
0100 0011 => ‘C’
C = $43
0100 0011 => MSB odd parity
Value (Keyboard)
-----
ASCII Table (7-bit)
(ASCII = American Standard Code for Information Interchange)
Decimal
-------
Octal
-----
Hex
---
Binary
------
Choi = $43 $68 $6F $69
0100 0011 => ‘C’
C = $43
0100 0011 => MSB odd parity
1100 0011 => MSB even parity
Value (Keyboard)
-----
ASCII Table (7-bit)
(ASCII = American Standard Code for Information Interchange)
Decimal
-------
Octal
-----
Hex
---
Binary
------
Value (Keyboard)
-----
Choi = $43 $68 $6F $69
0100 0011 => ‘C’
C = $43
0100 0011 => MSB odd parity
1100 0011 => MSB even parity
0110 1111 => ‘o’
o = $6F
1110 1111 => MSB odd parity
0110 1111 => MSB even parity
100 0011 => ‘C’ = $43
0100 0011 => MSB odd parity
1100 0011 => MSB even parity
110 1111 => ‘o’ = $6F
1110 1111 => MSB odd parity
0110 1111 => MSB even parity
P it Circuit
Parity
Ci it
D7
D6
D5
D4
D3
D2
D1
D0 = P
0100 0011 => ‘C’ = $43
0100 0011 => MSB odd parity
1100 0011 => MSB even parity
D6
D5
D4
D3
D2
D1
D0
=P
1
0
0
0
0
1
1
=P
Even Parity
1
1
0
0
0
0
1
1
D7
D6
D5
D4
D3
D2
D1
D0
Z=A
B