Question

Convert the bicimal to base ten
101.111two

Answer 1

The binary number 101.111two is converted to decimal (base ten) by multiplying each digit by 2 to the power of its position, resulting in the decimal number 23.875.

Step-by-step explanation:

The question is asking to convert a binary number to base ten. The binary number in question is 101.111 (binary). To convert a binary number to a decimal (base ten) number, each digit is multiplied by 2 raised to the power of its position, counting from right to left and starting with the power of zero just after the decimal point.

Here is the conversion step by step:

• 1 (furthest right) = 1 × 2^0 = 1
• 1 (second from right) = 1 × 2^1 = 2
• 1 (third from right) = 1 × 2^2 = 4
• 0 (to the left of the decimal point) = 0 × 2^3 = 0
• 1 (to the left of the decimal point) = 1 × 2^4 = 16

Now, let's also convert the fractional part to the right of the decimal point:

• 1 (first to the right of decimal) = 1 × 2^-1 = 0.5
• 1 (second to the right of decimal) = 1 × 2^-2 = 0.25
• 1 (third to the right of decimal) = 1 × 2^-3 = 0.125

Finally, add up all the values:

16 + 0 + 4 + 2 + 1 + 0.5 + 0.25 + 0.125 = 23.875

Therefore, the binary number 101.111 in base ten is 23.875.