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Express the following numbers in decimal: (a) * (10110. 0101) 2 (b) * (16. 5) 16 (c) * (26. 24) 8 (d) (dada. B) 16 (e) (1010. 1101) 2

User Cewood
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1 Answer

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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.

User Dubas
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