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Task/Four-bit-adder/Lua/four-bit-adder.lua

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+-- Build XOR from AND, OR and NOT
+function xor (a, b) return (a and not b) or (b and not a) end
+
+-- Can make half adder now XOR exists
+function halfAdder (a, b) return xor(a, b), a and b end
+
+-- Full adder is two half adders with carry outputs OR'd
+function fullAdder (a, b, cIn)
+    local ha0s, ha0c = halfAdder(cIn, a)
+    local ha1s, ha1c = halfAdder(ha0s, b)
+    local cOut, s = ha0c or ha1c, ha1s
+    return cOut, s
+end
+
+-- Carry bits 'ripple' through adders, first returned value is overflow
+function fourBitAdder (a3, a2, a1, a0, b3, b2, b1, b0) -- LSB-first
+    local fa0c, fa0s = fullAdder(a0, b0, false)
+    local fa1c, fa1s = fullAdder(a1, b1, fa0c)
+    local fa2c, fa2s = fullAdder(a2, b2, fa1c)
+    local fa3c, fa3s = fullAdder(a3, b3, fa2c)
+    return fa3c, fa3s, fa2s, fa1s, fa0s -- Return as MSB-first
+end
+
+-- Take string of noughts and ones, convert to native boolean type
+function toBool (bitString)
+    local boolList, bit = {}
+    for digit = 1, 4 do
+        bit = string.sub(string.format("%04d", bitString), digit, digit)
+        if bit == "0" then table.insert(boolList, false) end
+        if bit == "1" then table.insert(boolList, true) end
+    end
+    return boolList
+end
+
+-- Take list of booleans, convert to string of binary digits (variadic)
+function toBits (...)
+    local bStr = ""
+    for i, bool in pairs{...} do
+        if bool then bStr = bStr .. "1" else bStr = bStr .. "0" end
+    end
+    return bStr
+end
+
+-- Little driver function to neaten use of the adder
+function add (n1, n2)
+    local A, B = toBool(n1), toBool(n2)
+    local v, s0, s1, s2, s3 = fourBitAdder( A[1], A[2], A[3], A[4],
+                                            B[1], B[2], B[3], B[4] )
+    return toBits(s0, s1, s2, s3), v
+end
+
+-- Main procedure (usage examples)
+print("SUM", "OVERFLOW\n")
+print(add(0001, 0001)) -- 1 + 1 = 2
+print(add(0101, 1010)) -- 5 + 10 = 15
+print(add(0000, 1111)) -- 0 + 15 = 15
+print(add(0001, 1111)) -- 1 + 15 = 16 (causes overflow)