Exercise DET-01.03 – Binary arithmetic

Prof. Dr. Thorsten Jungmann (last updated 2026-11-02)

Relates to DET-01 Introduction to the module and its content

Task

Calculate the following sums and differences of unsigned binary numbers. The numbers have 4 bits in a) and d) and 8 bits in the other subtasks. Check each result by converting the numbers into the decimal number system, and state for each addition whether a carry out occurs.

Addition: a) $011 1_{2} + 010 1_{2}$ , b) $1100101 1_{2} + 0101111 0_{2}$ , c) $0101110 1_{2} + 0011011 0_{2}$

Subtraction: d) $111 0_{2} - 010 1_{2}$ , e) $1010001 1_{2} - 0011011 0_{2}$ , f) $1100000 1_{2} - 0101101 0_{2}$

Solution

a) $110 0_{2}$ (7 + 5 = 12; no carry out)
b) $10010100 1_{2}$ (203 + 94 = 297; carry out)
c) $1001001 1_{2}$ (93 + 54 = 147; no carry out)
d) $100 1_{2}$ (14 − 5 = 9)
e) $0110110 1_{2}$ (163 − 54 = 109)
f) $0110011 1_{2}$ (193 − 90 = 103)

▶️ Full worked solution

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Exercise DET-01.03 – Binary arithmetic

Task

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