Bit slice

Also called: ALU slice, 1-bit ALU slice, one-bit slice

One bit position of a multi-bit circuit such as an ALU. An n-bit ALU is n identical slices side by side, sharing control lines and chaining carries.

Many datapath circuits do the same thing to every bit. Instead of designing an n-bit circuit all at once, you design one bit slice, the circuit for a single bit position, and copy it n times.

A 1-bit slice of the course's ALU contains:

a controlled inverter on B (an XOR driven by SUB)
a full adder for A, the possibly inverted B, and the carry from the slice to its right
the logic units, here an AND gate and an OR gate
a result multiplexer that picks one unit's output as Y, using the opcode

To make n bits:

place n slices side by side
connect every slice to the same opcode lines
chain the carries: slice i's carry-out feeds slice i + 1's carry-in, and SUB drives slice 0's carry-in
add the flag logic after the slices, looking at all n outputs and the top two carries

Bit slicing is why designs scale: a 4-bit and a 64-bit ALU differ only in how many slices you place. In the 1970s, companies even sold 4-bit ALU slice chips that designers cascaded into wider processors.

Worked example

Example

Two slices computing 0101 − 0011

Opcode 11 (SUB), so SUB = 1 in every slice. Follow the two lowest slices.

1.
Slice 0: A0 = 1, B0 = 1 is inverted to 0, carry-in = SUB = 1. 1 + 0 + 1 = 10₂, so its sum is 0 and it carries 1.
2.
Slice 1: A1 = 0, B1 = 1 is inverted to 0, carry-in 1. 0 + 0 + 1 = 1, so its sum is 1 and it carries 0.
3.
F1 = 1, so each slice's MUX outputs the sum: Y1 = 1, Y0 = 0.
4.
The full result is 0010 = 2 = 5 − 3, and the low two bits match.

Common mistakes

Giving each slice its own opcode. All slices share the same select lines.
Forgetting that slice 0's carry-in must come from SUB.
Computing the flags inside each slice. N, Z, C and V look at the whole word.

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Bit slice is taught in Adders and ALUs.

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