Convert the following binary numbers into octal and hexadecimal numbers. (i) 1110001000 (ii) 110110101 (iii) 1010100 (iv) 1010.1001

Convert the following binary numbers into octal and hexadecimal numbers.

(i) 1110001000

(ii) 110110101

(iii) 1010100

(iv) 1010.1001

Let's convert the given binary numbers into both octal and hexadecimal systems:

(i) $ 1110001000 $

1. Binary to Octal:

   • Grouping bits from right to left in groups of 3: $ 1 ~\underline{110} ~\underline{001} ~\underline{000} $

   • Corresponding octal digits: $ 1 \ 6 \ 1 \ 0 $

   • Result: $ (1110001000)_2 = (1610)_8 $

2. Binary to Hexadecimal:

   • Grouping bits from right to left in groups of 4: $\underline{1110} \underline{0010} \ 000 $

   • Corresponding hex digits: $ E \ 2 \ 0 $

   • Result: $ (1110001000)_2 = (E20)_{16} $

(ii) $ 110110101 $

1. Binary to Octal:

   • Grouping bits from right to left in groups of 3: $ \underline{001} ~\underline{101} ~\underline{101} $

   • Corresponding octal digits: $ 1 \ 5 \ 5 $

   • Result: $ (110110101)_2 = (155)_8 $

2. Binary to Hexadecimal:

   • Grouping bits from right to left in groups of 4: $\underline{1101} ~\underline{1010} ~ 1 $

   • Corresponding hex digits: $ D \ A \ 1 $

   • Result: $ (110110101)_2 = (1DA)_{16} $

(iii) $ 1010100 $

1. Binary to Octal:

   • Grouping bits from right to left in groups of 3: $ \underline{001} ~\underline{010} ~\underline{100} $

   • Corresponding octal digits: $ 1 \ 2 \ 4 $

   • Result: $ (1010100)_2 = (124)_8 $

2. Binary to Hexadecimal:

   • Grouping bits from right to left in groups of 4: $\underline{1010}~ \underline{100} $

   • Corresponding hex digits: $ A \ 4 $

   • Result: $ (1010100)_2 = (54)_{16} $

(iv) $ 1010.1001 $

1. Binary to Octal:

   • Grouping integer part from right to left in groups of 3 and fractional part from left to right in groups of 3: $ 1 \underline{010} \cdot \underline{100} $

   • Corresponding octal digits: $ 1 \ 2 \cdot 4 $

   • Result: $ (1010.1001)_2 = (12.4)_8 $

2. Binary to Hexadecimal:

   • Grouping integer part from right to left in groups of 4 and fractional part from left to right in groups of 4: $ \underline{1010} \cdot \underline{1001} $

   • Corresponding hex digits: $ A \cdot 9 $

   • Result: $ (1010.1001)_2 = (A.9)_{16} $

Summary:

1. $ (1110001000)_2 = (1610)_8 = (E20)_{16} $

2. $ (110110101)_2 = (155)_8 = (1DA)_{16} $

3. $ (1010100)_2 = (124)_8 = (54)_{16} $

4. $ (1010.1001)_2 = (12.4)_8 = (A.9)_{16} $