Answer to Question #335273 in Combinatorics | Number Theory for Maneo

Question

Work out the following and give answers in the indicated bases/codes. (Show your ALL working):

a. 1660₈ – 530₁₆ in base 8

b. AB.75₁₆ – 830.5₁₀ in base 2

c. 4028₁₀ + 475.08₁₆ in base 16

d. 1024₁₀ – 11010111₂ in base 2 

Answer 1

a) $1660_8-530_{16}=1660_8-2460_8=-600_8$

$530_{16}=(0101)_2(0011)_2(0000)_2=10100110000_2=(10)(100)(110)(000)_2=2460_8$

b) $\text{AB}.75_{16}-830.5_{10}=1010100000110110.1_2$

$\text{AB}.75=\text{10}_{10}\text{11}_{10}.7_{10}5_{10}=1010_{2}1011_20111_20101_2=1010101101110101_2$

$830.5_{10}=2\cdot 415+2^{-1}=2\cdot207+2+2^{-1}=2^3\cdot 103+2^2+2+2^{-1}=2^4\cdot 51+2^3+2^2+2+2^{-1}=2^5\cdot 25+2^4+2^3+2^2+2+2^{-1}=2^8\cdot 3+2^5+ 2^4+2^3+2^2+2+2^{-1}=2^9+2^8+2^5+ 2^4+2^3+2^2+2+2^{-1}=1100111110.1_2$

c) $4028_{10}-475.08_{16}=\text{B}46.\text{F}8_{16}$

$4028_{10}=16\cdot 251+12=16\cdot(16\cdot 15+11)+12=16^2\cdot 15+16\cdot 11+12=\text{FBC}_{16}$

d) $1024_{10}-11010111_2= 10000000000_2-11010111_2=1100101001_2$

$1024_{10}=2^{10}=10000000000_2$