3 of 3Q3.a) Convert each binary number to decimal, octal and hexadecimal: [14 marks]i. 101010101110ii. 101011000.011iii. 10111011.1110

Sure, let's convert each binary number to decimal, octal and hexadecimal:

i. Binary: 101010101110

• Decimal: To convert binary to decimal, we start from the rightmost digit (also known as the least significant bit) and keep multiplying each digit with powers of 2 (starting from 0). So, the decimal equivalent of 101010101110 is (02^0) + (12^1) + (12^2) + (02^3) + (12^4) + (02^5) + (12^6) + (02^7) + (12^8) + (02^9) + (12^10) + (12^11) = 2734.

• Octal: To convert binary to octal, we group the binary number into sets of three (from right to left) and then replace each group with its octal equivalent. So, the octal equivalent of 101010101110 is 5256.

• Hexadecimal: To convert binary to hexadecimal, we group the binary number into sets of four (from right to left) and then replace each group with its hexadecimal equivalent. So, the hexadecimal equivalent of 101010101110 is AAAE.

ii. Binary: 101011000.011

• Decimal: The integer part is converted the same way as before. For the fractional part, we start from the rightmost digit and keep multiplying each digit with powers of 2 (starting from -1 and going to the left). So, the decimal equivalent of 101011000.011 is 688.375.

• Octal: The integer part is converted the same way as before. For the fractional part, we group the binary number into sets of three (from right to left) and then replace each group with its octal equivalent. So, the octal equivalent of 101011000.011 is 1300.14.

• Hexadecimal: The integer part is converted the same way as before. For the fractional part, we group the binary number into sets of four (from right to left) and then replace each group with its hexadecimal equivalent. So, the hexadecimal equivalent of 101011000.011 is 2B0.6.

iii. Binary: 10111011.1110

• Decimal: The integer part is converted the same way as before. For the fractional part, we start from the rightmost digit and keep multiplying each digit with powers of 2 (starting from -1 and going to the left). So, the decimal equivalent of 10111011.1110 is 187.875.

• Octal: The integer part is converted the same way as before. For the fractional part, we group the binary number into sets of three (from right to left) and then replace each group with its octal equivalent. So, the octal equivalent of 10111011.1110 is 273.7.

• Hexadecimal: The integer part is converted the same way as before. For the fractional part, we group the binary number into sets of four (from right to left) and then replace each group with its hexadecimal equivalent. So, the hexadecimal equivalent of 10111011.1110 is BB.E.