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| Boolean
Algebra |
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Logic gates and circuits |
The
"AND" gate, the "OR" gate and the "NOT"
gate |
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Binary number system |
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Binary
to decimal conversion |
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Decimal
to binary conversion |
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Logic
Gates and Circuits |
| There
are exactly three basic electronic circuits called logic gates
each of which correspond to one of the three Boolean (binary) operators, “and,” “or,” and
“not” having the same properties. |
| AND
gate |
| a |
b |
a
·
b |
| 0 |
0 |
0 |
| 1 |
0 |
0 |
| 0 |
1 |
0 |
| 1 |
1 |
1 |
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OR
gate |
| a |
b |
a
+ b |
| 0 |
0 |
0 |
| 1 |
0 |
1 |
| 0 |
1 |
1 |
| 1 |
1 |
1 |
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NOT gate (or
invertor) |
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| Logic
circuits used in digital computers are built up from logic
gates. We want to know the output y
of a logic
circuit for all possible combinations of input bits.
The value of the output is shown at the resultant column of the
corresponding truth table. |
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| Binary
Number System |
| The
binary number system uses digits, 0 and 1 to represent numbers.
A binary number can be therefore represented by any sequence of
bits
(binary digits). |
| The tables
show binary representations of integers from 0 to 19 with corresponding place values of bits. |
| Decimal
number |
Binary
number |
| 24 |
23
|
22 |
21
|
20 |
| 0 |
0 |
0 |
0 |
0 |
0 |
| 1 |
0 |
0 |
0 |
0 |
1 |
| 2 |
0 |
0 |
0 |
1 |
0 |
| 3 |
0 |
0 |
0 |
1 |
1 |
| 4 |
0 |
0 |
1 |
0 |
0 |
| 5 |
0 |
0 |
1 |
0 |
1 |
| 6 |
0 |
0 |
1 |
1 |
0 |
| 7 |
0 |
0 |
1 |
1 |
1 |
| 8 |
0 |
1 |
0 |
0 |
0 |
| 9 |
0 |
1 |
0 |
0 |
1 |
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| Decimal
number |
Binary
number |
| 24 |
23
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22 |
21
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20 |
| 10 |
0 |
1 |
0 |
1 |
0 |
| 11 |
0 |
1 |
0 |
1 |
1 |
| 12 |
0 |
1 |
1 |
0 |
0 |
| 13 |
0 |
1 |
1 |
0 |
1 |
| 14 |
0 |
1 |
1 |
1 |
0 |
| 15 |
0 |
1 |
1 |
1 |
1 |
| 16 |
1 |
0 |
0 |
0 |
0 |
| 17 |
1 |
0 |
0 |
0 |
1 |
| 18 |
1 |
0 |
0 |
1 |
0 |
| 19 |
1 |
0 |
0 |
1 |
1 |
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| Binary
to decimal conversion: Any binary number can be converted to its
decimal equivalent by writing it in a place-value notation, i.e. as the sum of products of each
digit with place value of that digit. |
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| Example: |
=
1 · 26 + 0
· 25
+ 1 · 24 + 1 · 23
+ 1 · 22 + 0 ·
21
+ 1 · 20 = |
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= 64 + 0
+ 16 + 8
+ 4 +
0 + 1
= 93 |
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| Decimal
to binary conversion: |
| To convert a decimal number to its
binary equivalent divide given decimal and each successive
quotient by 2 noting remainders from right to left, that is from
the lowest place value to the higher. |
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The remainders can only be 0 and 1 since divisions are by 2. The
division ends by the quotient
zero. |
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| 113 |
÷ |
2 |
= |
1
1 1 1 0 0 0 1 |
| 56 |
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| Beginning
Algebra Contents |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
