9.Express the following numbers in decimal:
(a) (10110.0101)₂ (b) (16.5)₁₆ (c) (26.24)₈ (d) (DADA.B)₁₆ (e) (1010.1101)₂
(a) (10110.0101)₂ = 1*2⁴+0*2³+1*2²+1*2¹+0*2⁰+0*2ˉ¹+1*2ˉ²+0*2ˉ³+1*2ˉ⁴
= 16+0+4+2+0+0+0.25+0.0625
= (22.3125)₁₀
(b) (16.5)₁₆ = 1*16¹+ 6*16⁰+ 5*16ˉ¹
= 16+6+0.3125
= (22.3125)₁₀
(c) (26.24)₈ = 2*8¹+6*8⁰+2*8ˉ¹+4*8ˉ²
=16+6+0.25+0.25
= (22.50)₁₀
(d) (DADA.B)₁₆ = 13*16³+10*16²+13*16¹+10*16⁰+11*16ˉ¹
= 53,248+2560+208+10+0.6875
= (56026.6875)₁₀
(e) (1010.1101)₂ = 1*2³+0*2²+1*2¹+0*2⁰+1*2ˉ¹+1*2ˉ²+0*2ˉ³+1*2ˉ⁴
= 8+0+2+0+0.5+0.25+0+0.125
= (10.8125)₁₀