Conversion of Decimal Number to any Radix Number

CONVERSION OF DECIMAL NUMBER TO ANY RADIX NUMBER

Conversion of decimal number to other number system have to follow two steps

(i) Convert the integer parts by successive division method.

(ii) Convert the fraction part by successive multiplication method.

In successive division we repeatedly divide the integer part of the decimal number by radix (r) until quotient is zero. The remainder of each division becomes the numerical value of the new radix.

Decimal to Binary

Problem: 6

Convert decimal number (29)₁₀ to binary equivalent.

Solution:

Divide 29 by 2

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(29)₁₀ => (11101)₂

Problem: 7

Convert decimal number 225 to binary value.

Solution:

N = (225)₁₀

(225)₁₀ => (11100001)₂

Successive Multiplication for Fractional Part:

The fractional decimal numbers to another radix number is obtained using a successive multiplication method. The number is multiplied by the radix of new number, producing a product in that has integer part and fractional part. The integer part of product becomes a numeral in the new radix. The fractional part is again multiplied by the radix. This process is repeated until fractional part reaches zero.

Problem: 8

Convert (0.825)₁₀ decimal number to binary number.

Solution:

(0.825) × 2 = 1.650 = 0.650 = 1

(0.650) × 2 = 1.300 = 0.300 = 1

(0.300) × 2 = 0.600 = 0.600 = 0

(0.600) × 2 = 1.200 = 0.200 = 1

(0.200) × 2 = 0.400 = 0.400 = 0

(0.400) × 2 = 0.800 = 0.800 = 0 ↓

(0.825)₁₀ => (110100... )₂

Problem: 9

Convert (14.25)₁₀ to binary number system.

Solution:

Integer part (14) fraction part (0.25)

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0.25 × 2 = 0.50 = 0

0.50 × 21.00 = 1

.01

(14.25)₁₀ => (1110.01)₂

Conversion of Decimal to Octal Number

Problem: 10

Convert decimal number 37.42 to octal number.

Solution:

(0.42)₁₀

0.4 × 8 = 3.2 → 3

0.2 × 8 = 1.6 → 1

0.6 × 8 = 4.8 → 4

0.8 × 8 = 6.4 = 6

0.4 × 8 = 3.2 = 2 ↓

(37.42)₁₀ => (45.31463)₈

Problem: 11

(752.63)₁₀ convert to octal number system.

Solution:

0.63 × 8 = 5.04 = 5

0.04 × 8 = 0.32 = 0

0.32 × 8 = 2.56 = 2

0.56 × 8 = 4.48 = 4

0.48 × 8 = 3.84 = 3 ↓

(752) => (1360)₈

 (752.63)₁₀ => (1360.50243)₈

Problem: 12

Convert decimal number 225 to octal number system.

Solution:

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(225)₁₀ = (341)₈

Decimal to Hexadecimal Number System

Problem: 13

Convert (225)₁₀ to hexa decimal number system.

Solution:

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(225)₁₀ → (E1)₁₆

Problem: 14

Convert decimal number 1938.257 to hexa decimal number system.

Integer part:

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(1938)₁₀ ⇒ (792)₁₆

Fractional part:

0.257 × 16 = 4.112 = 4

0.112 × 16 = 1.792 = 1

0.792 × 16 = 12.672 = C

0.672 × 16 = 10.752 = A  ↓

(0.257)₁₀ ⇒  0.41CA

(1938.257)₁₀ ⇒ (792.41 CA)₁₆