Conversion of Hexadecimal to any other Radix System

CONVERSION OF HEXADECIMAL TO ANY OTHER RADIX SYSTEM

Hexadecimal to Binary Number System

Before going to conversion between binary, octal and hexadecimal. We see the number of digits in serval number system. It is shown in Table 4.1.

Conversion from hexadecimal to binary each digit of the hexadecimal number is individually convert to its binary equivalent to get hexadecimal to binary conversion of the number.

Problem: 15

(4A8)₁₆ convert to binary number system.

 (Refer the table 4.1)

Binary number = (010010101000)₂

(4A8)₁₆ = (10010101000)₂

Problem: 16

(6B2.A3)₁₆ to binary number system.

Binary number = (011010110010.10100011)₂

(6 B2. A3)₁₆ = (11010110010.10100011)₂

Problem: 17

(A44.21)₁₆ convert to binary number system.

(A44.21)₁₆ = (10100100 0100. 0010 0001)₂

Hexadecimal to Octal Conversion

The following steps to convert hexa decimal to octal

(i) convert hexe decimal to binary number

(ii) then convert binary to octal number system

Problem: 18

Convert (2A)₁₆ to octal number system.

Step (i)

Step (ii)

Separate 3 digit from left side, the above binary number

(2A)₁₆ ⇒ (52)₈

Problem: 19

Convert (3AC.27)₁₆ to octal number system.

Step (i)

Binary number = 001,110, 101,100: 0010 0111

001, 110, 101, 100. 001, 001, 110

(1654.116)₈

(3AC. 27)₁₆ ⇒ (1654.116)₈

Hexadecimal to Decimal Conversion

Problem: 20

Convert the hexadecimal number (2AC5)₁₆ to decimal number system.

(2AC5)₁₆ = 2 × 16³ + 10 × 16² + 12 × 16¹ + 5 × 16⁰

= 8192 + 2560 + 192 + 5

= 10949

(2AC5)₁₆ = (10949)₁₀

Problem: 20

Convert the hexadecimal number (2AC5)₁₆ to decimal number system.

(2AC5)₁₆ = 2 × 16³ + 10 × 16² + 12 × 16¹ + 5 × 16⁰

= 8192 + 2560 + 192 + 5

= 10949

(2AC5)₁₆ = (10949)₁₀

Problem: 21

Convert the hexadecimal number (B42)₁₆ to decimal number system.

(B42)₁₆ = 11 × 16² + 4 × 16¹ + 2 × 16⁰

= 2816 + 64 + 2

(B42)₁₆ = (2882)₁₀