1.If A is represented as 65 in ASCII, what is the binary representation of the letter βBβ in the word βBATβ?
2.If A is 65 in ASCII, what is the binary representation of the entire word βBATβ?
3.How is the digit 9 in the number 99 represented in BCD, and what is its binary form?
4.What is the complete BCD representation of the number 99 in binary, and how does it differ from pure binary?
Β
1.
Answer: The letter βBβ in ASCII is 66, which in binary is 1000010.
Description:
- In ASCII, each character is assigned a decimal value:
- βAβ = 65
- βBβ = 66 (since it follows A in the alphabet)
- βTβ = 84
- To convert 66 (decimal) to binary:
- 66 Γ· 2 = 33 remainder 0
- 33 Γ· 2 = 16 remainder 1
- 16 Γ· 2 = 8 remainder 0
- 8 Γ· 2 = 4 remainder 0
- 4 Γ· 2 = 2 remainder 0
- 2 Γ· 2 = 1 remainder 0
- 1 Γ· 2 = 0 remainder 1
- Read remainders bottom to top: 1000010 (7 bits, standard for ASCII).
- ASCII typically uses 7 or 8 bits; with 8 bits, itβs 01000010 (leading zero added).
2.
Answer: The word βBATβ in ASCII binary is:
- B = 66 = 1000010
- A = 65 = 1000001
- T = 84 = 1010100
- Combined (7-bit per character): 1000010 1000001 1010100.
Description: - ASCII values:
- βBβ = 66 β Binary: 1000010 (divide 66 by 2 repeatedly: 33r0, 16r1, 8r0, 4r0, 2r0, 1r0, 0r1).
- βAβ = 65 β Binary: 1000001 (divide 65: 32r1, 16r0, 8r0, 4r0, 2r0, 1r0, 0r1).
- βTβ = 84 β Binary: 1010100 (divide 84: 42r0, 21r0, 10r1, 5r0, 2r1, 1r0, 0r1).
- Each character uses 7 bits in basic ASCII; with 8 bits, add a leading zero (e.g., 01000010 01000001 01010100).
- The binary string represents βBATβ as stored or transmitted in a computer.
3.
Answer: In BCD, the digit 9 is represented as 1001. For 99, each 9 is 1001, so itβs 1001 1001.
Description:
- BCD (Binary-Coded Decimal) encodes each decimal digit (0-9) using 4 bits:
- 0 = 0000, 1 = 0001, 2 = 0010, 3 = 0011, 4 = 0100, 5 = 0101, 6 = 0110, 7 = 0111, 8 = 1000, 9 = 1001.
- For the number 99, break it into individual digits: 9 and 9.
- First 9 = 1001 (binary for 9 in BCD).
- Second 9 = 1001 (same).
- Thus, one 9 from 99 is 1001 in BCD. The full number 99 is two sets of 4 bits, but this focuses on a single digitβs representation.
4.
Answer: The BCD representation of 99 is 1001 1001 (8 bits total). In pure binary, 99 is 1100011 (7 bits).
Description:
- BCD Conversion:
- In BCD, each decimal digit is encoded separately with 4 bits:
- 9 = 1001.
- 99 = 9 and 9 β 1001 (first 9) and 1001 (second 9) = 1001 1001.
- In BCD, each decimal digit is encoded separately with 4 bits:
- Pure Binary Conversion:
- Convert 99 to binary:
- 99 Γ· 2 = 49r1, 49 Γ· 2 = 24r1, 24 Γ· 2 = 12r0, 12 Γ· 2 = 6r0, 6 Γ· 2 = 3r0, 3 Γ· 2 = 1r1, 1 Γ· 2 = 0r1.
- Bottom to top: 1100011 (7 bits).
- Convert 99 to binary:
- Difference:
- BCD uses 8 bits (4 per digit) and directly represents each decimal digit, making it less efficient but easier for decimal display systems.
- Pure binary uses 7 bits, compacting the value into a single binary number, which is more efficient for computation but not digit-by-digit readable.