library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;

entity example is
  port (Reset      : in  std_logic;
        SysClk     : in  std_logic;
        zbroji     : in  std_logic;
        oduzmi     : in  std_logic;
        ulaz_broj  : in  std_logic;
        oduzima    : out std_logic;
        ucitanPrvi : out std_logic;
        broj1      : out std_logic
        );

end example;

architecture Behavioral of example is

  -- Delayed version of input signals (1 clock cycle delay)
  signal zbroji_d : std_logic;
  signal oduzmi_d : std_logic;

  signal zbrojiRE : std_logic;
  signal oduzmiRE : std_logic;

begin

  -- Generate 1 clock cycle delayed version of
  -- signals we want to detect the rising edge
  -- Assumes active high reset
  -- Note: You should only use the rising_edge macro
  -- on an actual global or regional clock signal. FPGA's and
  -- ASICs place timing constraints on defined clock signals
  -- that make it possible to use rising_edge, otherwise, we have
  -- to generate our own rising edge signals by comparing delayed
  -- versions of a signal with the current signal.
  -- Also, with any respectable synthesizer / simulator using
  -- rising_edge is almos exactly the same as (clk'event and clk='1')
  -- except rising_edge only returns a '1' when the clock makes a
  -- valid '0' to '1' transition. (see link below)
  EdgeDetectProc : process (Reset, SysClk)
  begin
    if Reset = '1' then
      zbroji_d <= '0';
      oduzmi_d <= '0';
    elsif rising_edge(SysClk) then
      zbroji_d <= zbroji;
      oduzmi_d <= oduzmi;
    end if;
  end process EdgeDetectProc;

  -- Assert risinge edge signals for one clock cycle
  zbrojiRE <= '1' when zbroji = '1' and zbroji_d = '0' else '0';
  oduzmiRE <= '1' when oduzmi = '1' and oduzmi_d = '0' else '0';

  -- Assumes that you want a single cycle pulse on ucitanPrvi on the
  -- rising edege of zbroji or oduzmi;
  ucitanPrvi <= zbrojiRE or oduzmiRE;

  -- Based on your example, I can't tell what you want to do with the
  -- broj1 signal, but this logic will drive broj1 with ulaz_broj on
  -- either the zbroji or oduzmi rising edge, otherwise '0'.
  broj1 <= ulaz_broj when zbrojiRE = '1' else
           ulaz_broj when oduzmiRE = '1' else
           '0';

  -- Finally, it looks like you want to clear oduzima on the rising
  -- edge of zbroji and assert oduzima on the rising edge of
  -- oduzmi
  LatchProc : process (Reset, SysClk)
  begin
    if Reset = '1' then
      oduzima <= '0';
    elsif rising_edge(SysClk) then
      if zbrojiRE = '1' then
        oduzima <= '0';
      elsif oduzmiRE = '1' then
        oduzima <= '1';
      end if;
    end if;
  end process LatchProc;

end Behavioral;