1. (1010 0110)₂ = (166)₁₀
2. (145)₁₀ = (1001 0001)₂
3. (101 000 111 100)₂ = (5074)₈
4. (1111 1100 0011 0110)₂ = (FC36)₁₆
1. Convert the 8-binary binary expansion (1010 0110)₂ to a decimal expansion.
In order to solve this problem we have to use the expansion:
n = aₓbˣ + aₓ₋₁bˣ⁻¹ + ... + a₁b¹ + a₀
where b = 2, x = 8 - 1 = 7 due is a 8-binary
(1010 0110)₂ = 1 x 2⁷ + 0 x 2⁶ + 1 x 2⁵ + 0 x 2⁴ + 0 x 2³ + 1 x 2² + 1 x 2¹ + 0 x 2⁰
(1010 0110)₂ = 128 + 0 + 32 + 0 + 0 + 4 + 2 + 0
(1010 0110)₂ = (166)₁₀
2. Convert the following decimal expansion (145)₁₀ to an 8-bit binary expansion.
To solve this problem we have to use the divide by 2 process.
Since we are dividing by 2, when the dividend is an even number, the remainder will be 0, and when the dividend is an odd number the binary residual will be 1.
145 > 1 Less significant bit
145/2 = 72 > 0
72/ 2 = 36 > 0
36/2 = 18 > 0
18/2 = 9 > 1
9/2 = 4 > 0
4/2 = 2 > 0
2/2 = 1 > 1 Most significant bit
Then we order from the most significant bit to the less significant bit (from the bottom to the top) to obtain the 8-binary number:
(145)₁₀ = (1001 0001)₂
3. Convert the following hexadecimal expansion (A3C)₁₆ to an octal expansion.
To convert a hexadecimal expansion to an octal expansion we have to convert from hexadecimal to binary and then to octal using the table hexadecimal to binary and binary to octal.
Converting from hexadecimal to binary:
(A3C)₁₆
A = 1010, 3 = 0011 and C = 1100
(A3C)₁₆ = (1010 0011 1100)₂
Converting from binary to octal:
To convert binary to octal we have to order the binary expansion into group of 3-bits and use the table to convert binary to octal.
(1010 0011 1100)₂ = (101 000 111 100)₂
101 = 5, 000 = 0, 111 = 7 and 100 = 4
(101 000 111 100)₂ = (5074)₈
4. Convert the following binary expansion (1111 1100 0011 0110)₂ to a hexadecimal expansion.
To solve this exercise we have to use the binary to hexadecimal table.
(1111 1100 0011 0110)₂
1111 = F, 1100 = C, 0011 = 3 and 0110 = 6
(1111 1100 0011 0110)₂ = (FC36)₁₆
