Conveersion From 1 to 2 Family Nyc Code

Number Organisation Conversion

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There are many methods or techniques which can exist used to convert numbers from one base of operations to another. Nosotros'll demonstrate here the following −

• Decimal to Other Base of operations System
• Other Base System to Decimal
• Other Base System to Non-Decimal
• Shortcut method − Binary to Octal
• Shortcut method − Octal to Binary
• Shortcut method − Binary to Hexadecimal
• Shortcut method − Hexadecimal to Binary

Decimal to Other Base of operations Organisation

Steps

• Step one − Split the decimal number to be converted by the value of the new base of operations.

• Step 2 − Go the remainder from Step one equally the rightmost digit (to the lowest degree meaning digit) of new base number.

• Step 3 − Split up the quotient of the previous divide past the new base.

• Step 4 − Record the remainder from Step 3 as the next digit (to the left) of the new base number.

Repeat Steps three and 4, getting remainders from correct to left, until the quotient becomes cipher in Step 3.

The last remainder thus obtained will be the Most Significant Digit (MSD) of the new base number.

Case −

Decimal Number: 29₁₀

Computing Binary Equivalent −

Step	Operation	Upshot	Remainder
Step 1	29 / 2	fourteen	1
Footstep 2	14 / ii	seven	0
Step 3	7 / two	3	ane
Footstep 4	3 / 2	1	1
Step v	1 / 2	0	one

As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the outset rest becomes the To the lowest degree Significant Digit (LSD) and the last remainder becomes the Well-nigh Significant Digit (MSD).

Decimal Number − 29₁₀ = Binary Number − 11101_two.

Other Base System to Decimal Organisation

Steps

• Step 1 − Determine the cavalcade (positional) value of each digit (this depends on the position of the digit and the base of the number organization).

• Footstep 2 − Multiply the obtained column values (in Step 1) by the digits in the respective columns.

• Stride 3 − Sum the products calculated in Footstep two. The total is the equivalent value in decimal.

Case

Binary Number − 11101₂

Computing Decimal Equivalent −

Step	Binary Number	Decimal Number
Step 1	111012	((1 × ii4) + (one × iiiii) + (ane × 22) + (0 × 2i) + (one × 20))10
Pace 2	11101two	(16 + 8 + 4 + 0 + 1)10
Footstep 3	111012	2910

Binary Number − 11101₂ = Decimal Number − 29_x

Other Base System to Non-Decimal Arrangement

Steps

• Stride 1 − Convert the original number to a decimal number (base 10).

• Step 2 − Catechumen the decimal number and then obtained to the new base of operations number.

Instance

Octal Number − 25₈

Computing Binary Equivalent −

Footstep 1 − Convert to Decimal

Step	Octal Number	Decimal Number
Footstep 1	258	((2 × viiiane) + (v × 80))10
Pace ii	25eight	(16 + 5 )10
Pace 3	25viii	2110

Octal Number − 25_eight = Decimal Number − 21_x

Step 2 − Convert Decimal to Binary

Step	Operation	Result	Residual
Step 1	21 / 2	10	1
Step 2	10 / 2	5	0
Step 3	5 / 2	2	ane
Stride iv	two / 2	1	0
Stride five	1 / 2	0	1

Decimal Number − 21_x = Binary Number − 10101₂

Octal Number − 25₈ = Binary Number − 10101₂

Shortcut method - Binary to Octal

Steps

• Footstep ane − Separate the binary digits into groups of 3 (starting from the right).

• Step 2 − Catechumen each group of iii binary digits to one octal digit.

Example

Binary Number − 10101_ii

Calculating Octal Equivalent −

Step	Binary Number	Octal Number
Step one	10101two	010 101
Step two	101012	28 58
Pace three	101012	25eight

Binary Number − 10101₂ = Octal Number − 25₈

Shortcut method - Octal to Binary

Steps

• Stride 1 − Convert each octal digit to a 3 digit binary number (the octal digits may be treated every bit decimal for this conversion).

• Stride ii − Combine all the resulting binary groups (of 3 digits each) into a single binary number.

Instance

Octal Number − 25_viii

Computing Binary Equivalent −

Step	Octal Number	Binary Number
Pace 1	25eight	2x 510
Pace 2	258	0102 1012
Step 3	258	0101012

Octal Number − 25₈ = Binary Number − 10101₂

Shortcut method - Binary to Hexadecimal

Steps

• Step 1 − Divide the binary digits into groups of four (starting from the right).

• Step 2 − Catechumen each grouping of 4 binary digits to 1 hexadecimal symbol.

Instance

Binary Number − 10101₂

Computing hexadecimal Equivalent −

Pace	Binary Number	Hexadecimal Number
Step 1	101012	0001 0101
Step 2	101012	110 vten
Step three	101012	fifteenxvi

Binary Number − 10101₂ = Hexadecimal Number − 15_xvi

Shortcut method - Hexadecimal to Binary

Steps

• Footstep 1 − Convert each hexadecimal digit to a four digit binary number (the hexadecimal digits may be treated every bit decimal for this conversion).

• Step 2 − Combine all the resulting binary groups (of 4 digits each) into a unmarried binary number.

Case

Hexadecimal Number − 15_sixteen

Computing Binary Equivalent −

Step	Hexadecimal Number	Binary Number
Footstep 1	xv16	i10 510
Step 2	fifteen16	00012 0101ii
Step 3	1516	000101012

Hexadecimal Number − xv₁₆ = Binary Number − 10101₂

Useful Video Courses

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Source: https://www.tutorialspoint.com/computer_logical_organization/number_system_conversion.htm

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