IPA IP 2020 Question 62

10011011 — 155 is 128 + 16 + 8 + 2 + 1.

Subtract the largest power of two that fits, from 128 down:

• •155 − 128 = 27: the 128 bit is 1
• •64 and 32 do not fit into 27: those bits are 0
• •27 − 16 = 11: the 16 bit is 1
• •11 − 8 = 3: the 8 bit is 1
• •4 does not fit into 3: that bit is 0
• •3 − 2 = 1, then 1 − 1 = 0: the 2 and 1 bits are 1

Reading the bits from 128 to 1 gives 10011011.

Answer (a)

Why not others:

• •(b) 10110011 — 128 + 32 + 16 + 2 + 1 = 179
• •(c) 11001101 — 128 + 64 + 8 + 4 + 1 = 205
• •(d) 11011001 — 217; it is the answer written backwards, the slip made when the remainders of repeated division by 2 are read from first to last instead of last to first

Key rule: To convert decimal to binary, divide by 2 repeatedly and read the remainders from the last one up, or subtract powers of two from the largest; check by adding the weights of the 1 bits.

Basic Theory · AI-written, may contain errors