CSCI 255, ENGR 274, ECE 212 -- 12 October, 2000

Announcements

• Homework 6

carry-look-ahead adder

• generate, if both bits are 1
  • g_i = x_i y_i
• propagate, if one bit is 1
  • p_i = x_i XOR y_i
  • p_i = x_i + y_i
• carry out, if generating or propagating a carry in
  • c_i+1 = g_i + p_i c_i
• doing the math
  • c_i+1 = g_i + p_i c_i
  • c_i+2 = g_i+1 + p_i+1 g_i + p_i+1 p_i c_i
  • c_i+3 = g_i+2 + p_i+2 g_i+1 + p_i+2 p_i+1 g_i + p_i+2 p_i+1 p_i c_i
  • c_i+4 = g_i+3 + p_i+3 g_i+2 + p_i+3 p_i+2 g_i+1 + p_i+3 p_i+2 p_i+1 g_i + p_i+3 p_i+2 p_i+1 p_i c_i
• grouping some results
  • g_i,i+3 = g_i+3 + p_i+3 g_i+2 + p_i+3 p_i+2 g_i+1 + p_i+3 p_i+2 p_i+1 g_i
  • p_i,i+3 = p_i+3 p_i+2 p_i+1 p_i c_i
  • c_i+4 = g_i,i+3 + p_i,i+3 c_i
• wire it together in Figure 5.14
• A carry-lookahead spreadsheet

TTL components

• 4-bit adder with fast carry
• 4-bit BCD adder
• Look-ahead carry generator

The ALU

• Arithmetic-Logic Unit
• Typical pins
  • Two n-bit input words
  • One carry-in input
  • One n-bit output word
  • One carry-out output
  • Control inputs
• 4 bit TTL ALU

Combinational multipliers

• The Full Multi
• Partial products
  • A_15..0 = A_15..8 A_7..0
  • B_15..0 = B_15..8 B_7..0
  • A_15..0 × B_15..0 = (A_15..8 × B_15..8) << 16 + (A_15..8 × B_7..0 + A_7..0 × B_15..8) << 8 + (A_7..0 × B_7..0)