University:
Kentucky State University
Course:
COS 107 | Prob Solving, Logic & Design
Academic year:

2020
Views:

451

Pages:

10
Author:

marthamanayay9qr15

**Subject: Lec 1** **Date: 17-7-2022** **Numbering System:** 1. Binary: (0,1) 2. Octal: (0-7) 3. Decimal: (0-9) 4. Hexadecimal: (0-9, A-F) * **Most Significant Bit (MSB)** * **Least Significant Bit (LSB)** In a 32-bit number, bit number 0 is the LSB, bit number 31 is the MSB. **Converting from any numbering system to decimal:** (d_n...d_1d_0)_B -> ()_10 d_n * B^n + ... + d_1 * B^1 + d_0 * B^0 **Examples:** (27)_8 -> ()_10 7 * 8^0 + 2 * 8^1 = 7 + 16 = (23)_10 (27)_16 -> ()_10 7 * 16^0 + 2 * 16^1 = 7 + 32 = (39)_10 (1101)_2 -> ()_10 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 8 + 4 + 0 + 1 = (13)_10 **Subject** **Date** **No.** (1011.11)_2 -> ()_10 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 + 1 * 2^-1 + 1 * 2^-2 = 8 + 4 + 2 + 1 + 0.5 + 0.25 = (11.75)_10 (127.4)_8 -> ()_10 1 * 8^2 + 2 * 8^1 + 7 * 8^0 + 4 * 8^-1 = 64 + 16 + 7 + 0.5 = (87.5)_10 (B65F)_16 -> ()_10 11 * 16^3 + 6 * 16^2 + 5 * 16^1 + 15 * 16^0 = 46667_10 (2C-B3)_16 -> ()_10 2 * 16^1 + 12 * 16^0 + 11 * 16^-1 + 3 * 16^-2 = 32 + 12 + 11/16 + 3/256 = (44.264)_10 (63.25)_8 -> ()_10 6 * 8^1 + 3 * 8^0 + 2 * 8^-1 + 5 * 8^-2 = 51.328_10