ITPEC FE Morning October 2020 Question 1

0.00111 — dividing by 32 is dividing by 2⁵, which moves the binary point five places left.

• •7 in binary is 111
• •32 = 2⁵, so 7 ÷ 32 is 111 with the point moved five places left: 0.00111
• •Check: 0.00111₂ = 1/8 + 1/16 + 1/32 = 4/32 + 2/32 + 1/32 = 7/32

Answer (c)

Why not others:

• •(a) 0.001011 — equals 8/64 + 2/64 + 1/64 = 11/64, not 14/64
• •(b) 0.001101 — equals 8/64 + 4/64 + 1/64 = 13/64, one sixty-fourth short of 7/32
• •(d) 0.0111 — moves the point only four places, which gives 7/16

Key rule: Dividing by 2ⁿ shifts the binary point n places left, just as dividing by 10ⁿ does in decimal.

Basic Theory · AI-written, may contain errors