Explanation

(a)  ABI\(_{Hex}\) to octal

A=1010  B=1011 1=0001    -------- Step 1

= 101010110001\(_2\)

= 101=5   010=2    110=6    001=1  ---------- Step 2

=5261\(_{octal}\) ------ Step 3

= AB1\(_{16}\)

= Ax16\(^2\) + Bx16\(^1\) + 1x16\(^0\)

= 10 X 16\(_2\) + 11 X 16\(_1\) + 1 X 16\(_0\)

= 2560 + 176 + 1

= 2737\(_{10}\)

It has to be converted to octal

= 5261

(b)  1110111.101\(_2\) to Denary

64=1  32=1  16=1  8=0  4=1   2=1   1=1

64+32+16+0+4+2+1

=96+16+7
=96+23
=119

2nd step fractional part

-1 -2 -3

.1 0 1

=1x2\(^{-1}\) + 0x2\(^{-2}\) + 1x2\(^{-3}\)

= \(\frac{1}{2^1}\) +  \(\frac{0}{2^2}\) + \(\frac{1}{2^3}\)

= \(\frac{1}{4}\) + 0 + \(\frac{1}{8}\)

= \(\frac{5}{8}\)

= 0.625

: 1110111.101\(_2\) = 119.625

(c) 507\(_{octal}\) to Binary

5=101   0=000    9=111

=101000111\(_2\)

OR

507\(_8\) to decimal

=5x8\(^2\) + 0x8\(^1\) + 7x8\(^0\)

= 5x64+0+7

=327\(_{10}\)

Conversion to binary

327\(_{10}\) to binary

=101000111\(_2\)

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