Explain the four arithmetic systems used in digital circuits or systems and convert binary to decimal.

Alright Megastar — let's do this. Here are the answers for question 1: a) Explain the four arithmetic systems used in digital circuits or system. 1. Binary (Base 2): This system uses only two digits, 0 and 1. It is the fundamental language of digital computers and electronic circuits because it can be easily represented by two distinct states, such as on/off or high/low voltage. 2. Octal (Base 8): This system uses eight digits (0-7). It is often used as a compact way to represent binary numbers, as each octal digit corresponds to exactly three binary digits. 3. Decimal (Base 10): This is the standard number system used by humans, employing ten digits (0-9). Digital systems often convert inputs and outputs to decimal for user interaction. 4. Hexadecimal (Base 16): This system uses sixteen symbols (0-9 and A-F, where A represents 10, B is 11, and so on up to F for 15). It is widely used in computing as a shorthand for binary numbers, with each hexadecimal digit representing four binary digits, making it efficient for representing memory addresses and data. b) Convert the following to base 10: i) 0.1001_2 Step 1: Expand the binary number using powers of 2. 0.1001_2 = (1 × 2^-1) + (0 × 2^-2) + (0 × 2^-3) + (1 × 2^-4) Step 2: Calculate the values. = (1 × 0.5) + (0 × 0.25) + (0 × 0.125) + (1 × 0.0625) Step 3: Sum the results. = 0.5 + 0 + 0 + 0.0625 = 0.5625_10 ii) 1101.101_2 Step 1: Expand the binary number using powers of 2. 1101.101_2 = (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0) + (1 × 2^-1) + (0 × 2^-2) + (1 × 2^-3) Step 2: Calculate the values. = (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1) + (1 × 0.5) + (0 × 0.25) + (1 × 0.125) Step 3: Sum the results. = 8 + 4 + 0 + 1 + 0.5 + 0 + 0.125 = 13 + 0.625 = 13.625_10 iii) 0.1101_2 Step 1: Expand the binary number using powers of 2. 0.1101_2 = (1 × 2^-1) + (1 × 2^-2) + (0 × 2^-3) + (1 × 2^-4) Step 2: Calculate the values. = (1 × 0.5) + (1 × 0.25) + (0 × 0.125) + (1 × 0.0625) Step 3: Sum the results. = 0.5 + 0.25 + 0 + 0.0625 = 0.8125_10 c) Convert the following to base 16: i) 0.47_10 Step 1: Multiply the fractional part by 16 and record the integer part. 0.47 × 16 = 7.52 integer part 7 Step 2: Take the new fractional part and repeat the multiplication. 0.52 × 16 = 8.32 integer part 8 Step 3: Repeat for desired precision. 0.32 × 16 = 5.12 integer part 5 0.12 × 16 = 1.92 integer part 1 Step 4: Read the integer parts from top to bottom. 0.7851..._16 ii) 524_10 Step 1: Divide the integer by 16 and record the remainder. 524 ÷ 16 = 32 remainder 12 (C in hex) Step 2: Divide the quotient by 16 and record the remainder. 32 ÷ 16 = 2 remainder 0 Step 3: Divide the quotient by 16 and record the remainder. 2 ÷ 16 = 0 remainder 2 Step 4: Read the remainders from bottom to top. 20C_16 iii) 374_10 Step 1: Divide the integer by 16 and record the remainder. 374 ÷ 16 = 23 remainder 6 Step 2: Divide the quotient by 16 and record the remainder. 23 ÷ 16 = 1 remainder 7 Step 3: Divide the quotient by 16 and record the remainder. 1 ÷ 16 = 0 remainder 1 Step 4: Read the remainders from bottom to top. 176_16 This was your last free solve today. To unlock unlimited solves, type /upgrade!