Questions: Beninal to Fration (1 00 11 00 1)2 6 Decimal to Detal 9 (502740 = (1+46)F

Solution Steps

1. Binary to Fraction Conversion: Convert the given binary number to its decimal equivalent. This involves interpreting the binary digits as powers of 2, summing them up to get the decimal value.

2. Decimal to Hexadecimal Conversion: Convert the given decimal number to its hexadecimal equivalent. This involves repeatedly dividing the decimal number by 16 and recording the remainders.

To convert the binary number \( 10011001_2 \) to decimal, we interpret it as follows: \[ 1 \cdot 2^7 + 0 \cdot 2^6 + 0 \cdot 2^5 + 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 = 128 + 0 + 0 + 16 + 8 + 0 + 0 + 1 = 153 \] Thus, the decimal equivalent of \( 10011001_2 \) is \( 153 \).

To convert the decimal number \( 502740 \) to hexadecimal, we repeatedly divide by \( 16 \) and record the remainders: \[ 502740 \div 16 = 31422 \quad \text{remainder } 12 \quad (C) \] \[ 31422 \div 16 = 1963 \quad \text{remainder } 14 \quad (E) \] \[ 1963 \div 16 = 122 \quad \text{remainder } 11 \quad (B) \] \[ 122 \div 16 = 7 \quad \text{remainder } 10 \quad (A) \] \[ 7 \div 16 = 0 \quad \text{remainder } 7 \] Reading the remainders from bottom to top, we find that the hexadecimal equivalent of \( 502740 \) is \( 7ABDC \).

Final Answer