Express the binary number 1001.01112 as a decimal number.
1001.0111 in decimal form is 9.4375.
To convert a binary number to a decimal number, we will use the place value system. Each digit in a binary number represents a power of 2, beginning from right to left with 2^0, then 2^1, 2^2, and so on.
Let's break down the given binary number 1001.0111:
The whole number part is 1001 (reading from left to right):
1 * 2^3 = 1 * 8 = 8
0 * 2^2 = 0 * 4 = 0
0 * 2^1 = 0 * 2 = 0
1 * 2^0 = 1 * 1 = 1
So the whole number part (1001) in decimal is 8 + 0 + 0 + 1 = 9.
The fractional part is 0111 (reading from left to right):
0 * 2^-1 = 0 * 0.5 = 0
1 * 2^-2 = 1 * 0.25 = 0.25
1 * 2^-3 = 1 * 0.125 = 0.125
1 * 2^-4 = 1 * 0.0625 = 0.0625
So the fractional part (0111) in decimal is 0 + 0.25 + 0.125 + 0.0625 = 0.4375.
Therefore, the binary number 1001.0111 is equal to the decimal number 9.4375.
To convert a binary number to a decimal number, you need to understand the place value system of the binary system. Each digit in a binary number represents a power of 2.
In the binary number 1001.0111, the integer part (left of the decimal point) and the fractional part (right of the decimal point) are separated.
Starting from the integer part:
1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0 = 8 + 0 + 0 + 1 = 9
For the fractional part:
0 * 2^-1 + 1 * 2^-2 + 1 * 2^-3 + 1 * 2^-4 = 0 + 0.25 + 0.125 + 0.0625 = 0.4375
Adding the integer and fractional parts together:
9 + 0.4375 = 9.4375
Therefore, the decimal representation of the binary number 1001.0111 is 9.4375.