Answer:
(a) To convert from binary to decimal, we can use the formula:
decimal = a_0 * 2^0 + a_1 * 2^1 + a_2 * 2^2 + ... + a_n * 2^n
where a_i is the i-th digit of the binary number.
Using this formula, we can convert (10110.0101)2 to decimal as follows:
(10110.0101)2 = 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0 + 0 * 2^-1 + 1 * 2^-2 + 0 * 2^-3 + 1 * 2^-4
= 22.3125
Therefore, (10110.0101)2 = 22.3125 in decimal.
(b) To convert from hexadecimal to decimal, we can use the formula:
decimal = a_0 * 16^0 + a_1 * 16^1 + a_2 * 16^2 + ... + a_n * 16^n
where a_i is the i-th digit of the hexadecimal number.
Using this formula, we can convert (16.5)16 to decimal as follows:
(16.5)16 = 1 * 16^1 + 6 * 16^0 + 5 * 16^-1
= 22.5
Therefore, (16.5)16 = 22.5 in decimal.
(c) To convert from octal to decimal, we can use the formula:
decimal = a_0 * 8^0 + a_1 * 8^1 + a_2 * 8^2 + ... + a_n * 8^n
where a_i is the i-th digit of the octal number.
Using this formula, we can convert (26.24)8 to decimal as follows:
(26.24)8 = 2 * 8^1 + 6 * 8^0 + 2 * 8^-1 + 4 * 8^-2
= 22.375
Therefore, (26.24)8 = 22.375 in decimal.
(d) To convert from hexadecimal to decimal, we can use the formula:
decimal = a_0 * 16^0 + a_1 * 16
^1 + a_2 * 16^2 + ... + a_n * 16^n
where a_i is the i-th digit of the hexadecimal number.
Using this formula, we can convert (dada.B)16 to decimal as follows:
(dada.B)16 = 13 * 16^3 + 10 * 16^2 + 13 * 16^1 + 10 * 16^0 + 11 * 16^-1
= 56090.6875
Therefore, (dada.B)16 = 56090.6875 in decimal.
(e) To convert from binary to decimal, we can use the formula:
decimal = a_0 * 2^0 + a_1 * 2^1 + a_2 * 2^2 + ... + a_n * 2^n
where a_i is the i-th digit of the binary number.
Using this formula, we can convert (1010.1101)2 to decimal as follows:
(1010.1101)2 = 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 + 1 * 2^-1 + 1 * 2^-3
= 10.8125
Therefore, (1010.1101)2 = 10.8125 in decimal.