Study guide: Represent and Check Small Binary Data
Decode and encode unsigned values, distinguish pixel interpretation and test a toy parity check.
Ideas to explain in your own words
- Use powers of two to translate a small binary number.
- Construct unsigned four-bit numbers and reject an out-of-range value.
- Use bit positions as pixels instead of number places.
- Add an even-parity bit and state which changes the check can miss.
Watch your reasoning
- 1101 includes 8 + 4 + 1 = 13 and excludes the 2-place. Reading the characters as the decimal number 1,101 ignores the stated binary place values.
- 9 = 8 + 1, so include the 8 and 1 places and skip 4 and 2: 1001.
- Each row contains exactly one 1. The three filled cells form a diagonal, giving 3 total.
- The data already contains two 1s. Appending 0 preserves the even count; appending 1 would make it odd.
A worked review example
Decode four binary places: 1011 includes 8, skips 4, and includes 2 and 1. Its decimal value is 8 + 2 + 1 = 11. Encode a Value and Check the Range: 10 → 1010 → 8 + 2 = 10. Endpoints: 0 → 0000; 15 → 1111. Input 16 is out of range under this fixed four-bit contract. Decode a Tiny Binary Picture: Top row has 1 filled cell, middle row has 3, bottom row has 1: 1 + 3 + 1 = 5 filled cells. In row order the flat message is 010111010. Check a Simple Parity Rule: 10111 has four 1s: check passes. One-bit change 00111 has three 1s: check fails. Two-bit change 01111 has four 1s: check passes despite altered data. Passing parity does not prove the message is unchanged.
Make a practice plan
- Try the supplied lesson problems without looking at the answers.
- Compare your method with the worked examples and explain any correction.
- Use the new review cases, then complete the transfer task on paper or in your own document.