Integer part: 1111111₂ = 2⁶ + 2⁵ + 2⁴ + 2³ + 2² + 2¹ + 2⁰ = 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127 Fractional part: .11111₂ = 2^-1 + 2^-2 + 2^-3 + 2^-4 + 2^-5 = 0.5 + 0.25 + 0.125 + 0.0625 + 0.03125 = 0.96875 Add both parts: 127 + 0.96875

Formula for highest number with n bits: 2ⁿ - 1 Here, n = 11. Value = 2¹¹ - 1 Value = 2048 - 1 = 2047

We need to find n such that 2^n-1 ≤ 160 < 2ⁿ 2⁷ = 128 (Too small, 7 bits is not enough) 2⁸ = 256 (Enough, so 8 bits are required) Verification: 160₁₀ = 128 + 32 = 10100000₂ (which has exactly 8 digits).

Fractional weights: 2^-1=0.5, 2^-2=0.25, 2^-3=0.125, 2^-4=0.0625, 2^-5=0.03125... 0.0975 is smaller than 0.5, 0.25, and 0.125. Largest weight to fit: 2^-4 (0.0625) 0.0975 - 0.0625 = 0.035 Next weight to fit: 2^-5 (0.03125) 0.035 - 0.03125 = 0.00375 Next weight to fit: 2^-9 (0.001953125) 0.00375 - 0.001953125 = 0.001796875 This continues... The binary value is approx: 2^-4 + 2^-5 + 2^-9...

60 / 2 = 30 Remainder: 0 (LSB) 30 / 2 = 15 Remainder: 0 15 / 2 = 7 Remainder: 1 7 / 2 = 3 Remainder: 1 3 / 2 = 1 Remainder: 1 1 / 2 = 0 Remainder: 1 (MSB) Read remainders from bottom to top.

0.8732 × 2 = 1.7464 → Integer: 1 (MSB) 0.7464 × 2 = 1.4928 → Integer: 1 0.4928 × 2 = 0.9856 → Integer: 0 0.9856 × 2 = 1.9712 → Integer: 1 0.9712 × 2 = 1.9424 → Integer: 1 Read integers from top to bottom (approx 5 bits precision).

Carries: 1 1 1 1 1 1 1 1 + 1 1 1 1 --------- 1 1 1 1 0 Verification in decimal: 15 + 15 = 30 (which is 11110₂)

1 1 0 0 0 0 - 0 0 1 1 1 1 ------------- 1 0 0 0 0 1 Verification in decimal: 48 - 15 = 33 (which is 100001₂)

1 1 1 1 x 1 1 0 0 --------- 0 0 0 0 (1111 × 0) 0 0 0 0 (1111 × 0) 1 1 1 1 (1111 × 1) 1 1 1 1 (1111 × 1) ------------- 1 0 1 1 0 1 0 0 Verification in decimal: 15 × 12 = 180 (which is 10110100₂)

Original Binary: 1 1 0 0 0 1 1 1 1's Complement: 0 0 1 1 1 0 0 0 (Invert all bits) Add 1: + 1 --------------- 2's Complement: 0 0 1 1 1 0 0 1

Split into 4-bit groups: 1011 1011 Left group (1011) = 8 + 2 + 1 = 11 in decimal → 'B' in Hex Right group (1011) = 8 + 2 + 1 = 11 in decimal → 'B' in Hex Combine both hex digits.

Value of letters: A = 10, B = 11, C = 12 ABC₁₆ = (A × 16²) + (B × 16¹) + (C × 16⁰) = (10 × 256) + (11 × 16) + (12 × 1) = 2560 + 176 + 12 = 2748

8925 / 16 = 557 Remainder: 13 → D (LSD) 557 / 16 = 34 Remainder: 13 → D 34 / 16 = 2 Remainder: 2 → 2 2 / 16 = 0 Remainder: 2 → 2 (MSD) Read from bottom to top.

7777₈ = (7 × 8³) + (7 × 8²) + (7 × 8¹) + (7 × 8⁰) = (7 × 512) + (7 × 64) + (7 × 8) + (7 × 1) = 3584 + 448 + 56 + 7 = 4095 Shortcut: Since 7 is the max digit in base 8, 7777₈ = 8⁴ - 1 = 4096 - 1 = 4095

9999 / 8 = 1249 Remainder: 7 (LSD) 1249 / 8 = 156 Remainder: 1 156 / 8 = 19 Remainder: 4 19 / 8 = 2 Remainder: 3 2 / 8 = 0 Remainder: 2 (MSD) Read remainders from bottom to top.

Convert each digit independently: 7 → 111 7 → 111 7 → 111 Combine them together.

Group by 3 bits: 010 | 101 | 111 2 | 5 | 7 Combine the values.

1 → 0001 0 → 0000 5 → 0101 1 → 0001 Combine them sequentially.

First BCD string: 1001 1000 1001 = 9 1000 = 8 → 98₁₀ Second BCD string: 1000 0111 0000 1000 = 8 0111 = 7 0000 = 0 → 870₁₀