Perform the following conversions in the stated number bases; (a) AB1\(_{16}\) to Octal system (b)...

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\(_2\)