Exercise DET-01.02 – Converting numbers between number systems

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

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

Task

Convert each of the following numbers into the stated number system.

Binary → decimal: a) $11100101_2$, b) $101101001101_2$

Octal → decimal: c) $253_8$, d) $4726_8$

Hexadecimal → decimal: e) ${9E}_{16}$, f) ${C3A}_{16}$

Decimal → binary: g) $187_{10}$, h) $2854_{10}$

Decimal → octal: i) $201_{10}$, j) $3890_{10}$

Decimal → hexadecimal: k) $222_{10}$, l) $2788_{10}$

Binary → octal: m) $10011101_2$, n) $111010110001_2$

Octal → binary: o) $365_8$, p) $3042_8$

Binary → hexadecimal: q) $10100111_2$, r) $110100111000_2$

Hexadecimal → binary: s) ${5B}_{16}$, t) ${8F2}_{16}$

Octal → hexadecimal: u) $315_8$, v) $6524_8$

Hexadecimal → octal: w) ${E9}_{16}$, x) ${A7E}_{16}$

Solution

a) $11100101_2=229_{10}$; b) $101101001101_2=2893_{10}$
c) $253_8=171_{10}$; d) $4726_8=2518_{10}$
e) ${9E}_{16}=158_{10}$; f) ${C3A}_{16}=3130_{10}$
g) $187_{10}=10111011_2$; h) $2854_{10}=101100100110_2$
i) $201_{10}=311_8$; j) $3890_{10}=7462_8$
k) $222_{10}={\mathrm{DE}}_{16}$; l) $2788_{10}={AE4}_{16}$
m) $10011101_2=235_8$; n) $111010110001_2=7261_8$
o) $365_8=11110101_2$; p) $3042_8=11000100010_2$
q) $10100111_2={A7}_{16}$; r) $110100111000_2={D38}_{16}$
s) ${5B}_{16}=01011011_2$; t) ${8F2}_{16}=100011110010_2$
u) $315_8={\mathrm{CD}}_{16}$; v) $6524_8={D54}_{16}$
w) ${E9}_{16}=351_8$; x) ${A7E}_{16}=5176_8$

▶️ Full worked solution