How to calculate the base resistor of a transistor ?

[1233]

 Hi,

I was checking the pic up-down counter tutorial circuit, below.  I want to know how the base resistor was calculated.

 

transistor type: BC557AP  working as a switch

Base resistor: 4.7 k ohm  (R3, and R11)     <== How this was calculated ??

Display bus resisotors: 270 ohm  (I don't know if these are necessary in calculating R3 and R11)

 Thanks in advance

[1233]

any kind of help will be aprreciated

[supsup]

Rmax=(Vdd-Ube)/Ib, Ib=Id/hFE

Ube - Base to Emitter voltage (0,65V), Id - Display current, hFE - DC current gain BC557