Question $44$

NUMBER SYSTEM AND SWITCH LOGIC

a$)$ Write the first three $(3)$ letters of your surname in binary. $($Assume that $A=1,B=2,C=3,$ etc.$)$

$[3$ marks$]$

b$)$ An automatic teller machine $($ATM$)$ at the bank allows you to enter the amount of cash you wish to withdraw in decimal by pressing decimal digit symbol keys.

i$)$ Does the computer convert this decimal number into straight binary or BCD $?$

$[1$ mark$]$

ii$)$ Based on your previous answer for $($a$),$ fully articulate, how you arrived at that answer $[3$ marks$]$

c$)$ Convert the following values to their corresponding number system:

$[10$ marks$]$

i$){100011011011}_2$

ii$)72910$

iii$)2A{F}_{16}$

iv$)BA{6}_{16}$

$(,{)}_{10}$

v$){1001011000001110}_2$

$(,{)}_2$

$(,{)}_{10}$

$(,{)}_2$

$(,{)}_8$

d$)$ Use switch $($SPST$)$ logic circuits to represent the following logic statements:

i$)$ Output $=$A AND NOT $B$

$[2$ marks$]$

ii$)$ Output $=(AORB)ANDC$

$[3$ marks$]$

iii$)O$ utput $=$A AND $((BANDC)ORD)$

$[3$ marks$]$