Question

Convert $(1101100101011011{)}_2$to octal and hexadecimal representations.

Short answer

$(154533{)}_8$

$(\mathrm{D}95\mathrm{B}{)}_{16}$

Step-by-step solution

Step 1

$(1101100101011011{)}_2=2^{15}+2^{14}+2^{12}+2^{11}+2^8+2^6+2^4+2^3+2^1+2^0$

$=8^5+4*8^4+4*8^3+4*8^2+8^2+2*8^1+8^1+2*8^0+8^0=(154533{)}_8$

Step 2

$(1101100101011011{)}_2=2^{15}+2^{14}+2^{12}+2^{11}+2^8+2^6+2^4+2^3+2^1+2^0$

$=8*{16}^3+4*{16}^3+{16}^3+8+{16}^2+{16}^2+4*{16}^1+{16}^1+8*{16}^0+2*{16}^0+{16}^0=(\mathrm{D}95\mathrm{B}{)}_{16}$