(a) Convert directly into binary:
In this method, we perform successive divisions by 2 and record the remainders until the quotient becomes 0. The binary representation is obtained by writing the remainders in reverse order.

Decimal 431:
431 ÷ 2 = 215 remainder 1
215 ÷ 2 = 107 remainder 1
107 ÷ 2 = 53 remainder 1
53 ÷ 2 = 26 remainder 1
26 ÷ 2 = 13 remainder 0
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1

The binary representation of 431 is 110101111.

(b) Convert first to hexadecimal and then from hexadecimal to binary:
In this method, we convert the decimal number to hexadecimal and then convert the hexadecimal representation to binary.

Decimal 431:
431 in hexadecimal is 1AF.

Hexadecimal 1AF:
1AF in binary is 0001 1010 1111.

Comparing the two methods:
In terms of speed, converting directly into binary (Method a) is generally faster than converting first to hexadecimal and then from hexadecimal to binary (Method b). Method a requires performing successive divisions by 2, which can be done in a straightforward manner. On the other hand, Method b involves additional steps of converting to hexadecimal and then to binary, which require more computations.

Therefore, in this case, Method a (direct conversion to binary) is faster than Method b (conversion through hexadecimal).