Subtracting Hexadecimal Numbers

We are asked to find the difference when $(29.A)_{16}$ is subtracted from $(4F.B)_{16}$. This can be written as the calculation: $(4F.B)_{16} - (29.A)_{16}$.

To perform hexadecimal subtraction, we align the numbers vertically by their place values, similar to how we subtract decimal numbers. We work from right to left, starting with the digits after the hexadecimal point.

The subtraction problem is set up as follows:

$(4F.B)_{16}$
- $(29.A)_{16}$
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Subtracting Fractional Parts

We begin by subtracting the digits in the fractional part (the digits to the right of the hexadecimal point).

• Step 1: Subtract the rightmost digit: $B_{16}$ from $A_{16}$.
• Conversion to Decimal: To perform the subtraction, we can convert these hexadecimal digits to their decimal equivalents. $B_{16}$ equals 11 in decimal, and $A_{16}$ equals 10 in decimal.
• Calculation: We calculate the difference in decimal: $11 - 10 = 1$.
• Result in Hexadecimal: The result, 1 in decimal, is $1_{16}$ in hexadecimal.
• Therefore, the fractional part of our result is $(.1)_{16}$.

Subtracting Integer Parts

Next, we subtract the digits in the integer part (the digits to the left of the hexadecimal point), moving from right to left.

Step 2: Subtract the units place digits ($16^0$ place).

• Problem: Subtract $9_{16}$ from $F_{16}$.
• Conversion to Decimal: $F_{16}$ equals 15 in decimal.
• Calculation: We calculate the difference in decimal: $15 - 9 = 6$.
• Result in Hexadecimal: The result, 6 in decimal, is $6_{16}$ in hexadecimal.
• This is the units digit of our final answer.

Step 3: Subtract the sixteen's place digits ($16^1$ place).

• Problem: Subtract $2_{16}$ from $4_{16}$.
• Calculation: This subtraction can be done directly in hexadecimal or by converting to decimal ($4 - 2 = 2$). The result is $4_{16} - 2_{16} = 2_{16}$.
• Result in Hexadecimal: The result is $2_{16}$.
• This is the sixteen's digit of our final answer.

Combining the Results

Finally, we combine the results from the integer and fractional parts to form the complete hexadecimal number.

• The integer part is $(26)_{16}$.
• The fractional part is $(.1)_{16}$.
• Putting them together, we get the final result: $(26.1)_{16}$.

Thus, the subtraction $(4F.B)_{16} - (29.A)_{16}$ equals $(26.1)_{16}$.