This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Okay, let's think about this like we're using blocks or counting on our fingers, just like primary pupils learn. First, we need to understand what binary numbers mean in our normal counting system (base 10). In binary, each place value is double the one before it, starting from 1 on the right. ... 16, 8, 4, 2, 1 (these are the place values) Step 1: Change the first binary number (1110_2) into our normal number. c c c c c Place value: & 8 & 4 & 2 & 1 \\ Binary digit: & 1 & 1 & 1 & 0 \\ We have: • One group of 8 (1 × 8 = 8) • One group of 4 (1 × 4 = 4) • One group of 2 (1 × 2 = 2) • Zero groups of 1 (0 × 1 = 0) Add these up: 8 + 4 + 2 + 0 = 14. So, 1110_2 is the same as 14. Step 2: Change the second binary number (111_2) into our normal number. c c c c Place value: & 4 & 2 & 1 \\ Binary digit: & 1 & 1 & 1 \\ We have: • One group of 4 (1 × 4 = 4) • One group of 2 (1 × 2 = 2) • One group of 1 (1 × 1 = 1) Add these up: 4 + 2 + 1 = 7. So, 111_2 is the same as 7. Step 3: Add the two normal numbers together. Now we just add 14 + 7. 14 + 7 = 21. Step 4: Change our answer (21) back into a binary number. We need to find which binary place values add up to 21. We'll use the place values: 16, 8, 4, 2, 1. • Does 16 fit into 21? Yes. So we use one 16. 21 - 16 = 5 left over. Binary: 1 (for the 16s place) • Does 8 fit into 5? No. So we don't use an 8. Binary: 0 (for the 8s place) • Does 4 fit into 5? Yes. So we use one 4. 5 - 4 = 1 left over. Binary: 1 (for the 4s place) • Does 2 fit into 1? No. So we don't use a 2. Binary: 0 (for the 2s place) • Does 1 fit into 1? Yes. So we use one 1. 1 - 1 = 0 left over. Binary: 1 (for the 1s place) Putting the binary digits together from left to right (from the 16s place down to the 1s place), we get 10101_2. The final answer is 10101_2. 3 done, 2 left today. You're making progress.