Solve the following addition problems and express the following base ten numbers in base two.

Here are the solutions to your questions. 1) Solve the following a) 67433+4899+5432 Step 1: Add the first two numbers. 67433 + 4899 = 72332 Step 2: Add the result to the third number. 72332 + 5432 = 77764 The sum is 77764. b) 5324+8765+6543 Step 1: Add the first two numbers. 5324 + 8765 = 14089 Step 2: Add the result to the third number. 14089 + 6543 = 20632 The sum is 20632. 2) Express the following in base two. a) 15_ten Step 1: Divide 15 by 2 repeatedly and note the remainders. 15 ÷ 2 = 7 remainder 1 7 ÷ 2 = 3 remainder 1 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Step 2: Read the remainders from bottom to top. 15_ten = 1111_two b) 16_ten Step 1: Divide 16 by 2 repeatedly and note the remainders. 16 ÷ 2 = 8 remainder 0 8 ÷ 2 = 4 remainder 0 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Step 2: Read the remainders from bottom to top. 16_ten = 10000_two c) 18_ten Step 1: Divide 18 by 2 repeatedly and note the remainders. 18 ÷ 2 = 9 remainder 0 9 ÷ 2 = 4 remainder 1 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Step 2: Read the remainders from bottom to top. 18_ten = 10010_two d) 20_ten Step 1: Divide 20 by 2 repeatedly and note the remainders. 20 ÷ 2 = 10 remainder 0 10 ÷ 2 = 5 remainder 0 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Step 2: Read the remainders from bottom to top. 20_ten = 10100_two 3) Express the following correct to two significant figures. a) 3.4631 Step 1: Identify the first two significant figures, which are 3 and 4. Step 2: Look at the digit immediately after the second significant figure (6). Since 6 5, round up the second significant figure. 3.4631 ≈ 3.5 b) 54.621 Step 1: Identify the first two significant figures, which are 5 and 4. Step 2: Look at the digit immediately after the second significant figure (6). Since 6 5, round up the second significant figure. 54.621 ≈ 55 c) 532.64 Step 1: Identify the first two significant figures, which are 5 and 3. Step 2: Look at the digit immediately after the second significant figure (2). Since 2 < 5, keep the second significant figure as it is and replace subsequent digits before the decimal point with zeros. 532.64 ≈ 530 d) 43.5567 Step 1: Identify the first two significant figures, which are 4 and 3. Step 2: Look at the digit immediately after the second significant figure (5). Since 5 5, round up the second significant figure. 43.5567 ≈ 44 4) Binary arithmetic i) 10011_two + 111_two Step 1: Align the numbers and add column by column from right to left. c c c c c & 1 & 0 & 0 & 1 & 1_two \\ + & & & 1 & 1 & 1_two \\ Step 2: Perform binary addition. 1+1=10_two (write 0, carry 1) 1+1+1=11_two (write 1, carry 1) 0+1=1_two (write 1) 0+0=0_two (write 0) 1+0=1_two (write 1) c c c c c c & 1 & 0 & 0 & 1 & 1_two \\ + & & & & 1 & 1 & 1_two \\ 1 & 0 & 1 & 1 & 1 & 0_two \\ The sum is 101110_two. ii) 11111_two + 10011_two Step 1: Align the numbers and add column by column from right to left. c c c c c c & 1 & 1 & 1 & 1 & 1_two \\ + & 1 & 0 & 0 & 1 & 1_two \\ Step 2: Perform binary addition. 1+1=10_two (write 0, carry 1) 1+1+1=11_two (write 1, carry 1) 1+0+1=10_two (write 0, carry 1) 1+0+1=10_two (write 0, carry 1) 1+1+1=11_two (write 1, carry 1) c c c c c c c & 1 & 1 & 1 & 1 & 1_two \\ + & 1 & 0 & 0 & 1 & 1_two \\ 1 & 1 & 0 & 0 & 1 & 0_two \\ The sum is 110010_two. iii) 101_two × 11_two Step 1: Multiply 101_two by the rightmost digit of 11_two (which is 1). 101_two × 1_two = 101_two Step 2: Multiply 101_two by the leftmost digit of 11_two (which is 1), shifting one position to the left. 101_two × 1_two = 101_two (shifted becomes 1010_two) Step 3: Add the partial products. c c c c c & & 1 & 0 & 1_two \\ × & & & 1 & 1_two \\ & & 1 & 0 & 1_two \\ + & 1 & 0 & 1 & 0_two \\ 1 & 1 & 1 & 1_two \\ The product is 1111_two. 5) a. Define Binary numbers. Binary numbers are a numeral system that uses only two symbols, typically 0 and 1, to represent numerical values. This base-2 system is fundamental to digital electronics and computer science, where 0 and 1 correspond to the "off" and "on" states of electrical switches. b. Write five binary numbers you know. Here are five binary numbers: • 0_two • 1_two • 10_two • 11_two • 100_two That's 2 down. 3 left today — send the next one.