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Electronics Catlog
DIC Catlog

Number System
Conversions Between Number System
Arithematic Operations
1's & 2's Complement
Gray Codes
Arithmetic Circuits
Logical Gates and Truth Table Funtions
Boolean Expressions
Boolean Algebra
Karnaugh Map
Encoder & Decoder
TTL Circuits
555 Timer
Flip Flops
RS Flip - Flop
JK Flip - Flop
D Flip - Flop
Shift Register
Schmitt Trigger
Asynchronous Counters
Synchronous Counters
Digital - Analog Conversion
Data Flow
Memory Drives
Electronics Equation
Resistor Color Codes

Arithmetic Operations

Binary Addition

    Addition is a form of counting in which one quantity is added to another. The following definitions identify the basic terms of addition:

AUGEND - The quantity to which an addend is added

ADDEND - A number to be added to a preceding number

SUM - The result of an addition (the sum of 5 and 7 is 12)

    Let's start by adding two binary bits. Since each bit has only two possible values, 0 or 1, there are only four possible combinations of inputs. These four possibilities, and the resulting sums, are:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

Example 1

Binary Addition Example1

Example 2

Binary Addtion Example3

Example 3

Binary Addtion Example3

Subtraction of Binary Numbers

    The following definitions identify the basic terms you will need to know to understand subtraction operations:

SUBTRACT - To take away, as a part from the whole or one number from another

MINUEND - The number from which another number is to be subtracted

SUBTRAHEND - The quantity to be subtracted

REMAINDER, or DIFFERENCE - That which is left after subtraction

    Now that you are familiar with the addition of binary numbers, subtraction will be easy. The following are the four rules that you must observe when subtracting:

Binary Subtraction Example1

The following example (101102 - 11002) demonstrates the four rules of binary subtraction:

Binary Subtraction Example2

    Rule 4 presents a different situation because you cannot subtract 1 from 0. Since you cannot subtract 1 from 0 and have a positive difference, you must borrow the 1 from the next higher order column of the minuend. The borrow may be indicated as shown below:

    1 from the next higher order column of the minuend. The borrow may be indicated as shown below:

Binary Subtraction Example3

    Now observe the following method of borrowing across more than one column in the example, 10002 - 12:

Binary Subtraction Example4

Binary Multiplication

Example 1

Binary Multiplication Example1

Example 2

Binary Multiplication Example3

Example 3

Binary Multiplication Example3