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Number conversions 33 to binary etc.

Short answer

33 decimal is 100001 binary. (11000011)₂ equals 195 decimal. (1001)₂ + (0111)₂ = (10000)₂, which is 16 decimal.

Convert the following: i) 33(10) to binary ii) (1100 0011)2 to decimal iii) Add (1001)2 and (0111)2

i) 33₁₀ to binary

33 ÷ 2 = 16 r1, 16 → 8 r0, 8 → 4 r0, 4 → 2 r0, 2 → 1 r0, 1 → 0 r1. Read upward: 100001.

(33)₁₀ = (100001)₂

ii) (1100 0011)₂ to decimal

128 + 64 + 2 + 1 = 195

(11000011)₂ = (195)₁₀

iii) (1001)₂ + (0111)₂

   1001   (9)
 + 0111   (7)
 ------
  10000   (16)

Bit by bit: 1+1 = 0 carry 1; 0+1+1 = 0 carry 1; 0+1+1 = 0 carry 1; 1+0+1 = 0 carry 1; final carry 1.

Answer: (10000)₂ = 16₁₀

✓ Answer checked by Claude Opus 5.5 (high effort)

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