Chapter 2: Data Representation
1. Decimal to Binary & Hexadecimal
Q.1 Convert to Binary
(i) 13: Repeated division by 2.
13 ÷ 2 = 6 (R1), 6 ÷ 2 = 3 (R0), 3 ÷ 2 = 1 (R1), 1 ÷ 2 = 0 (R1)
Answer: (13)₁₀ = (1101)₂
(ii) 106:
106→53(R0)→26(R1)→13(R0)→6(R1)→3(R0)→1(R1)→0(R1)
Answer: (106)₁₀ = (1101010)₂
(iii) 3.25:
Int: 3 = 11₂. Frac: 0.25×2 = 0.5(0), 0.5×2 = 1.0(1)
Answer: (3.25)₁₀ = (11.01)₂
Q.8 & Q.9 Convert to Hexadecimal
423: 423 ÷ 16 = 26 (R7), 26 ÷ 16 = 1 (R10/A), 1 ÷ 16 = 0 (R1)
Answer: (423)₁₀ = (1A7)₁₆
72905: 72905÷16=4556(R9), 4556÷16=284(RC), 284÷16=17(RC), 17÷16=1(R1)
Answer: (72905)₁₀ = (11CC9)₁₆
2. Binary/Hex to Decimal
Q.2 (i) 10010₂: 1×2⁴ + 0×2³ + 0×2² + 1×2¹ + 0×2⁰ = 16 + 2 = 18
Comprehensive Number System Conversions & Binary Arithmetic
•
•
•
•
•
•
