Question

Simplify the expression
using rules of Boolean algebra. [4 marks]
d) Compute the value of 3AB16-43510-6178 using 1’s complement arithmetic
leaving your final answer in Octal. [5 Marks]
f (a,b,c) = a. b + a.(b + c)+(a. b. (c + b. d)+ a. b). c. d

Answer 1

As per the given question,

We have to determine the subtraction, 3AB16-43510-6178

Now, hexadecimal to binary conversion of the given terms

$(3AB16)_{16}=(00111010101100010110)_2$

similarly, $(43510)_{16}=(01000011010100010000)_2$

$(6178)_{16}=(0110000101111000)_2$

Now subtraction of $3AB16-43510$ using 1s compliment,

$\Rightarrow (00111010101100010110)_2-(01000011010100010000)_2=(1000100111111010)_2$

$\Rightarrow (1000100111111010)_2-(0110000101111000)_2=(10100010000010)_2$

Hence octet conversion of the given terms will be 24202