📘 number systems

1. **Problem Statement:** Evaluate the following subtractions in base 8 (octal): a) $424_8 - 373_8$

1. The problem is to convert the decimal number 10 to its binary equivalent. 2. The formula or method used is to divide the decimal number by 2 repeatedly and record the remainders

1. **Problem Statement:** Convert the decimal number 330 (base 10) to binary (base 2), then to octal (base 8), and finally to hexadecimal (base 16). 2. **Step 1: Convert from decim

1. The problem is to convert the hexadecimal number $\text{D42C3}_{16}$ into its binary equivalent. 2. Each hexadecimal digit corresponds to exactly 4 binary digits (bits). This is

1. **Problem:** Convert the binary number 101101 to decimal. 2. **Formula and rules:** To convert a binary number to decimal, multiply each bit by $2^{position}$ where position sta

1. The problem asks for the decimal equivalent of the binary number $1101_2$. 2. To convert a binary number to decimal, use the formula:

1. **State the problem:** Subtract the base five numbers $314_5$ and $233_5$. 2. **Recall the subtraction rules in base five:** In base five, digits range from 0 to 4. If a digit i

1. The problem is to write the number 24 in Roman numerals. 2. Roman numerals use letters to represent values: I=1, V=5, X=10, L=50, C=100, D=500, M=1000.

1. The problem is to add the numbers 206 and 109 and then convert the result into Roman numerals. 2. First, add the numbers: $$206 + 109 = 315$$.

1. The problem asks to convert the number 100000 to its decimal value. 2. Since 100000 is already written in decimal notation (base 10), no conversion is needed.

1. The problem is to express the decimal number 5213 in octal (base 8). 2. To convert a decimal number to octal, we repeatedly divide the number by 8 and record the remainders.

1. The problem is to divide the octal number 665 by 6. 2. First, convert the octal number 665 to decimal. Octal digits represent powers of 8, so:

1. The problem involves understanding the relationship between hexadecimal numbers and their decimal equivalents, as well as interpreting the given data. 2. Hexadecimal (base 16) n

1. The problem involves understanding the relationship between hexadecimal, decimal, and binary numbers as shown in the table. 2. Hexadecimal (base 16) numbers use digits 0-9 and l

1. **State the problem:** Convert the number 312 from base 4 to base 10. 2. **Formula and explanation:** To convert a number from base $b$ to base 10, use the formula:

1. **Convert (85.375)₁₀ to binary (base 2):** Step 1: Convert the integer part 85 to binary.

1. Convert $(85.375)_{10}$ to binary (base 2). - Separate the integer and fractional parts: $85$ and $0.375$.

1. **State the problem:** Divide the base-4 number $(321230)_4$ by $(123)_4$ and show the whole process. 2. **Convert both numbers from base 4 to base 10:**

1. The problem is to simplify the expression $2_2$. 2. The notation $2_2$ typically means the number 2 in base 2.

1. Convert 262 to binary, octal, and hexadecimal: - Binary: Divide 262 by 2 repeatedly and record remainders:

1. The problem is to understand the conversion of the binary number $10111_2$ to its decimal equivalent and to discuss the representation of decimal floating point numbers in octal